4D N=4 TV Specific GL2R Central Charges.nb
Requires N4TVUpToTildeTilde.m that includes
BosonSolutions[tt1,tt2][ss]: all possible ways of closing the Tilde-Tilde Tensor and Tilde-Tilde Vector algebra as shown in 4D N=4 TV No Closure
1) Among the BosonSolutions[tt1,tt2][ss], selects the solution as reported in 1812.04236
3) Calculates the central charges for this particular solution. These are the central charges reported in 1812.04236

$RecursionLimit=Infinity

Load Data from the Save Point of 4D N=4 TV No Closure

SetDirectory[NotebookDirectory[]];

<<N4TVUpToTildeTilde.m;

Lagrangian is Satisfied, untilded and tilded algebras are separably satisfied

DLFinal[1]==(DLFinal[2]/.LagrangianParameters)=={{0,0,0,0},{0,0,0,0}}

Table[AlgebraDDResult[1,1][Index],{Index,1,14}]==Table[True,{Index,1,14}]

ClosureResult[2,2][1] == ClosureResult[2,2][2] == True

Solutions are BosonSolutions[tt1,tt2][ss][[1]]

BosonSolutions[2,2][2][[1]]

ThisOneLooksGood: a particularly simple solution

ThisOneLooksGood =Join[BosonSolutions[2,2][1][[600]],BosonSolutions[2,2][2][[400]]]

Table[PrintSigmaProduct[Table[V[nn][ii,jj],{ii,1,2},{jj,1,2}]/.VtoPauli/.ThisOneLooksGood],{nn,1,12}]

TeXForm[%]

aTable = {a1,a2,a3,a4,a5};

DeleteCases[Table[a[Index] == (aTable[[Index]]/.ThisOneLooksGood),{Index,1,5}],a[_]==0]

bTable = {b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11};

DeleteCases[Table[b[Index] == (bTable[[Index]]/.ThisOneLooksGood),{Index,1,11}],b[_]==0]

Algebra {(Subscript[D, a]^i),(Subscript[(OverTilde[D]), b]^j)} MUST have central charges as proved in “4D N=4 TV No Closure.nb”

tt1 = 1, tt2 = 2, Zgen[lfn,fn][i,j] := ((Z[lfn,fn])^ij)  for central charge coding ease

Clear[tt1,tt2,ss]
tt1 = 1
tt2 = 2

ZGen[lfn,fn][i_,j_]:= z[lfn,fn,0] (δ^ij) + z[lfn,fn,1] ((((σ^1)))^ij)+ i z[lfn,fn,2] ((((σ^2)))^ij)+z[lfn,fn,3] ((((σ^3)))^ij)

ZGen[lfn_,fn_][ii_,jj_] := z[lfn,fn,0] KroneckerDelta[ii,jj] + z[lfn,fn,1] sigma[1][[ii,jj]] + I z[lfn,fn,2] sigma[2][[ii,jj]]+z[lfn,fn,3] sigma[3][[ii,jj]]

{(Subscript[D, a]^i),(Subscript[(OverTilde[D]), b]^j)}A= 2i ((Z[1,1])^ij)(Subscript[((γ^μ)), ab])(∂_μ)(OverTilde[A]) +2((Z[1,2])^ij)(Subscript[((γ^5)(γ^μ)), ab])(∂_μ)(OverTilde[B]) +2i ((Z[1,3])^ij)(Subscript[C, ab])(OverTilde[F])+2 ((Z[1,4])^ij)(Subscript[((γ^5)), ab])(OverTilde[G])+2i ((Z[1,5])^ij)(Subscript[((γ^μ)), ab])(∂_μ)φ+((Z[1,6])^ij)(Subscript[(ϵ^(μναβ))((γ^5)(Subscript[γ, μ])), ab])(∂_ν)(Subscript[B, αβ])+i ((Z[1,7])^ij)(Subscript[((Subscript[γ, μ])), ab])(∂_ν)(B^(μν))  
FieldNumber = 1

LocalField = A[t,x,y,z];
LocalFieldNumber = 1;
CentralChargeList[LocalFieldNumber] = Table[z[LocalFieldNumber,FieldNumber,sigmaNumber],{FieldNumber,1,7},{sigmaNumber,0,3}]//Flatten

Z[LocalFieldNumber][ii_,jj_][aa_,bb_]:=2 I ZGen[LocalFieldNumber,1][ii,jj]Sum[γdown[mu][[aa,bb]]D[At[t,x,y,z],Ϛ[mu]],{mu,0,3}]+2 ZGen[LocalFieldNumber,2][ii,jj]Sum[γ5γdown[mu][[aa,bb]]D[Bt[t,x,y,z],Ϛ[mu]],{mu,0,3}] + 2 I ZGen[LocalFieldNumber,3][ii,jj]Cmetric[[aa,bb]]Ft[t,x,y,z]+ 2 ZGen[LocalFieldNumber,4][ii,jj]γ5down[[aa,bb]]Gt[t,x,y,z]+2 I ZGen[LocalFieldNumber,5][ii,jj]Sum[γdown[mu][[aa,bb]]D[φ[t,x,y,z],Ϛ[mu]],{mu,0,3}] + ZGen[LocalFieldNumber,6][ii,jj]Sum[ϵup[mu,nu,ap,bt]γ5γstdowndown[mu][[aa,bb]]D[Bmn[ap,bt][t,x,y,z],Ϛ[nu]],{mu,0,3},{nu,0,3},{ap,0,3},{bt,0,3}]+I ZGen[LocalFieldNumber,7][ii,jj]Sum[γstdowndown[mu][[aa,bb]]D[Bmnup[mu,nu][t,x,y,z],Ϛ[nu]],{mu,0,3},{nu,0,3}]

ZTable[LocalFieldNumber] = Table[Z[LocalFieldNumber][ii,jj][aa,bb],{ii,1,2},{aa,1,4},{jj,1,2},{bb,1,4}];

AlgebraDDMinusClosure[tt1,tt2][LocalFieldNumber]=(Collect[(AlgebraDD[tt1,tt2][LocalField] - ZTable[LocalFieldNumber])/.LagrangianParameters/.VtoPauli,FieldListWithDerivatives,Simplify]);

AlgebraDDEqs[tt1,tt2][LocalFieldNumber] = DeleteCases[Table[(Coefficient[AlgebraDDMinusClosure[tt1,tt2][LocalFieldNumber][[ii,aa,jj,bb]],FieldListWithDerivatives[[FieldListIndex]]])==0,{ii,1,2},{aa,1,4},{jj,1,2},{bb,1,4},{FieldListIndex,1,Length[FieldListWithDerivatives]}]//Simplify//Flatten,True]//DeleteDuplicates;

Length[AlgebraDDEqs[tt1,tt2][LocalFieldNumber]]

ZSolutions[LocalFieldNumber] = Solve[AlgebraDDEqs[tt1,tt2][LocalFieldNumber],CentralChargeList[LocalFieldNumber]]//Flatten

Investigate a particular solution

ZSolutions[LocalFieldNumber]/.BosonSolutions[2,2][1][[1]]/.BosonSolutions[2,2][2][[1]]/.(1/(Sqrt[-1-((cv[5][1])^2)]))-> (-I/ (Sqrt[1+((cv[5][1])^2)]))/.cv[10][0]-> -I cv[5][1]/. (Sqrt[-1-((cv[5][1])^2)])-> I  (Sqrt[1+((cv[5][1])^2)])/.cv[12][3]-> -I (Sqrt[1+((cv[5][1])^2)])/.(1/(Sqrt[-1-((cv[5][1])^2)]))-> (-I/ (Sqrt[1+((cv[5][1])^2)]))/.cv[5][1]-> I//PowerExpand

Investigate another

ZSolutions[LocalFieldNumber]/.ThisOneLooksGood

{(Subscript[D, a]^i),(Subscript[(OverTilde[D]), b]^j)}A= 2i ((Z[1,1])^ij)(Subscript[((γ^μ)), ab])(∂_μ)(OverTilde[A]) +2((Z[1,2])^ij)(Subscript[((γ^5)(γ^μ)), ab])(∂_μ)(OverTilde[B]) +2i ((Z[1,3])^ij)(Subscript[C, ab])(OverTilde[F])+2 ((Z[1,4])^ij)(Subscript[((γ^5)), ab])(OverTilde[G])+2i ((Z[1,5])^ij)(Subscript[((γ^μ)), ab])(∂_μ)φ+((Z[1,6])^ij)(Subscript[(ϵ^(μναβ))((γ^5)(Subscript[γ, μ])), ab])(∂_ν)(Subscript[B, αβ])+i ((Z[1,7])^ij)(Subscript[((Subscript[γ, μ])), ab])(∂_ν)(B^(μν))  
FieldNumber = 1

DeleteCases[Table[Z[LocalFieldNumber,nn]==PrintSigmaProduct[Table[ZGen[LocalFieldNumber,nn][ii,jj],{ii,1,2},{jj,1,2}]/.ZSolutions[LocalFieldNumber]/.ThisOneLooksGood],{nn,1,7}],Z[_,_]==0]
TeXForm[%]

Clear[LocalField,LocalFieldNumber]

{(Subscript[D, a]^i),(Subscript[(OverTilde[D]), b]^j)}B=2((Z[2,1])^ij)(Subscript[((γ^5)(γ^μ)), ab])(∂_μ)(OverTilde[A]) +2i ((Z[2,2])^ij)(Subscript[((γ^μ)), ab])(∂_μ)(OverTilde[B]) +2((Z[2,3])^ij)(Subscript[((γ^5)), ab])(OverTilde[F])+2 i ((Z[2,4])^ij)(Subscript[C, ab])(OverTilde[G])+2((Z[2,5])^ij)(Subscript[((γ^5)(γ^μ)), ab])(∂_μ)φ+i ((Z[2,6])^ij)(Subscript[(ϵ^(μναβ))((Subscript[γ, μ])), ab])(∂_ν)(Subscript[B, αβ])+((Z[2,7])^ij)(Subscript[((γ^5)(Subscript[γ, μ])), ab])(∂_ν)(B^(μν))  
 FieldNumber = 2

LocalField = B[t,x,y,z];
LocalFieldNumber = 2;
CentralChargeList[LocalFieldNumber] = Table[z[LocalFieldNumber,FieldNumber,sigmaNumber],{FieldNumber,1,7},{sigmaNumber,0,3}]//Flatten

Z[LocalFieldNumber][ii_,jj_][aa_,bb_]:=2 ZGen[LocalFieldNumber,1][ii,jj]Sum[γ5γdown[mu][[aa,bb]]D[At[t,x,y,z],Ϛ[mu]],{mu,0,3}]+2 I ZGen[LocalFieldNumber,2][ii,jj]Sum[γdown[mu][[aa,bb]]D[Bt[t,x,y,z],Ϛ[mu]],{mu,0,3}] + 2 ZGen[LocalFieldNumber,3][ii,jj]γ5down[[aa,bb]]Ft[t,x,y,z]+ 2 I ZGen[LocalFieldNumber,4][ii,jj]Cmetric[[aa,bb]]Gt[t,x,y,z]+2 ZGen[LocalFieldNumber,5][ii,jj]Sum[γ5γdown[mu][[aa,bb]]D[φ[t,x,y,z],Ϛ[mu]],{mu,0,3}] + I ZGen[LocalFieldNumber,6][ii,jj]Sum[ϵup[mu,nu,ap,bt]γstdowndown[mu][[aa,bb]]D[Bmn[ap,bt][t,x,y,z],Ϛ[nu]],{mu,0,3},{nu,0,3},{ap,0,3},{bt,0,3}]+ZGen[LocalFieldNumber,7][ii,jj]Sum[γ5γstdowndown[mu][[aa,bb]]D[Bmnup[mu,nu][t,x,y,z],Ϛ[nu]],{mu,0,3},{nu,0,3}]

ZTable[LocalFieldNumber] = Table[Z[LocalFieldNumber][ii,jj][aa,bb],{ii,1,2},{aa,1,4},{jj,1,2},{bb,1,4}];

AlgebraDDMinusClosure[tt1,tt2][LocalFieldNumber]=(Collect[(AlgebraDD[tt1,tt2][LocalField] - ZTable[LocalFieldNumber])/.LagrangianParameters/.VtoPauli,FieldListWithDerivatives,Simplify]);

AlgebraDDEqs[tt1,tt2][LocalFieldNumber] = DeleteCases[Table[(Coefficient[AlgebraDDMinusClosure[tt1,tt2][LocalFieldNumber][[ii,aa,jj,bb]],FieldListWithDerivatives[[FieldListIndex]]])==0,{ii,1,2},{aa,1,4},{jj,1,2},{bb,1,4},{FieldListIndex,1,Length[FieldListWithDerivatives]}]//Simplify//Flatten,True]//DeleteDuplicates;

Length[AlgebraDDEqs[tt1,tt2][LocalFieldNumber]]

ZSolutions[LocalFieldNumber] = Solve[AlgebraDDEqs[tt1,tt2][LocalFieldNumber],CentralChargeList[LocalFieldNumber]]//Flatten

ZSolutions[LocalFieldNumber]/.ThisOneLooksGood

{(Subscript[D, a]^i),(Subscript[(OverTilde[D]), b]^j)}B=2((Z[2,1])^ij)(Subscript[((γ^5)(γ^μ)), ab])(∂_μ)(OverTilde[A]) +2i ((Z[2,2])^ij)(Subscript[((γ^μ)), ab])(∂_μ)(OverTilde[B]) +2((Z[2,3])^ij)(Subscript[((γ^5)), ab])(OverTilde[F])+2 i ((Z[2,4])^ij)(Subscript[C, ab])(OverTilde[G])+2((Z[2,5])^ij)(Subscript[((γ^5)(γ^μ)), ab])(∂_μ)φ+i ((Z[2,6])^ij)(Subscript[(ϵ^(μναβ))((Subscript[γ, μ])), ab])(∂_ν)(Subscript[B, αβ])+((Z[2,7])^ij)(Subscript[((γ^5)(Subscript[γ, μ])), ab])(∂_ν)(B^(μν))  
 FieldNumber = 2

DeleteCases[Table[Z[LocalFieldNumber,nn]==PrintSigmaProduct[Table[ZGen[LocalFieldNumber,nn][ii,jj],{ii,1,2},{jj,1,2}]/.ZSolutions[LocalFieldNumber]/.ThisOneLooksGood],{nn,1,7}],Z[_,_]==0]
TeXForm[%]

Clear[LocalField,LocalFieldNumber]

{(Subscript[D, a]^i),(Subscript[(OverTilde[D]), b]^j)}F=2i ((Z[lfn,1])^ij)(Subscript[C, ab])□(OverTilde[A]) +2((Z[lfn,2])^ij)(Subscript[((γ^5)), ab])□ (OverTilde[B]) +2((iZ[lfn,3])^ij)(Subscript[((γ^μ)), ab])(∂_μ)(OverTilde[F])+2 ((Z[lfn,4])^ij)(Subscript[((γ^5)(γ^μ)), ab])(∂_μ)(OverTilde[G])+2i ((Z[lfn,5])^ij)(Subscript[C, ab])□φ+i ((Z[lfn,6])^ij)(Subscript[([(γ^α),(γ^β)]), ab])□(Subscript[B, αβ])+i ((Z[lfn,7])^ij)(Subscript[([(γ^α),(γ^μ)]), ab])(∂_μ)(∂^β)(Subscript[B, αβ])  
lfn = FieldNumber = 3

LocalField = F[t,x,y,z];
LocalFieldNumber = 3;
CentralChargeList[LocalFieldNumber] = Table[z[LocalFieldNumber,FieldNumber,sigmaNumber],{FieldNumber,1,7},{sigmaNumber,0,3}]//Flatten

Z[LocalFieldNumber][ii_,jj_][aa_,bb_]:=2 I ZGen[LocalFieldNumber,1][ii,jj]Cmetric[[aa,bb]]Lap[At[t,x,y,z]]+2 ZGen[LocalFieldNumber,2][ii,jj]γ5down[[aa,bb]]Lap[Bt[t,x,y,z]] + 2 I ZGen[LocalFieldNumber,3][ii,jj]Sum[γdown[mu][[aa,bb]]D[Ft[t,x,y,z],Ϛ[mu]],{mu,0, 3}]+ 2 ZGen[LocalFieldNumber,4][ii,jj]Sum[γ5γdown[mu][[aa,bb]]D[Gt[t,x,y,z],Ϛ[mu]],{mu,0, 3}]+2 I ZGen[LocalFieldNumber,5][ii,jj]Cmetric[[aa,bb]]Lap[φ[t,x,y,z]]+ I ZGen[LocalFieldNumber,6][ii,jj]Sum[CommuteGammadown[ap,bt][[aa,bb]]Lap[Bmn[ap,bt][t,x,y,z]],{ap,0,3},{bt,0,3}] + I ZGen[LocalFieldNumber,7][ii,jj]Sum[CommuteGammadown[ap,mu][[aa,bb]]D[UD[Bmn[ap,bt][t,x,y,z],Ϛ[bt]],Ϛ[mu]],{ap,0,3},{bt,0,3},{mu,0,3}]

ZTable[LocalFieldNumber] = Table[Z[LocalFieldNumber][ii,jj][aa,bb],{ii,1,2},{aa,1,4},{jj,1,2},{bb,1,4}];

AlgebraDDMinusClosure[tt1,tt2][LocalFieldNumber]=(Collect[(AlgebraDD[tt1,tt2][LocalField] - ZTable[LocalFieldNumber])/.LagrangianParameters/.VtoPauli,FieldListWithDerivatives,Simplify]);

AlgebraDDEqs[tt1,tt2][LocalFieldNumber] = DeleteCases[Table[(Coefficient[AlgebraDDMinusClosure[tt1,tt2][LocalFieldNumber][[ii,aa,jj,bb]],FieldListWithDerivatives[[FieldListIndex]]])==0,{ii,1,2},{aa,1,4},{jj,1,2},{bb,1,4},{FieldListIndex,1,Length[FieldListWithDerivatives]}]//Simplify//Flatten,True]//DeleteDuplicates;

Length[AlgebraDDEqs[tt1,tt2][LocalFieldNumber]]

ZSolutions[LocalFieldNumber] = Solve[AlgebraDDEqs[tt1,tt2][LocalFieldNumber],CentralChargeList[LocalFieldNumber]]//Flatten

ZSolutions[LocalFieldNumber]/.ThisOneLooksGood

{(Subscript[D, a]^i),(Subscript[(OverTilde[D]), b]^j)}F=2i ((Z[lfn,1])^ij)(Subscript[C, ab])□(OverTilde[A]) +2((Z[lfn,2])^ij)(Subscript[((γ^5)), ab])□ (OverTilde[B]) +2((iZ[lfn,3])^ij)(Subscript[((γ^μ)), ab])(∂_μ)(OverTilde[F])+2 ((Z[lfn,4])^ij)(Subscript[((γ^5)(γ^μ)), ab])(∂_μ)(OverTilde[G])+2i ((Z[lfn,5])^ij)(Subscript[C, ab])□φ+i ((Z[lfn,6])^ij)(Subscript[([(γ^α),(γ^β)]), ab])□(Subscript[B, αβ])+i ((Z[lfn,7])^ij)(Subscript[([(γ^α),(γ^μ)]), ab])(∂_μ)(∂^β)(Subscript[B, αβ])  
lfn = FieldNumber = 3

DeleteCases[Table[Z[LocalFieldNumber,nn]==PrintSigmaProduct[Table[ZGen[LocalFieldNumber,nn][ii,jj],{ii,1,2},{jj,1,2}]/.ZSolutions[LocalFieldNumber]/.ThisOneLooksGood],{nn,1,7}],Z[_,_]==0]

Clear[LocalField,LocalFieldNumber]

{(Subscript[D, a]^i),(Subscript[(OverTilde[D]), b]^j)}G= 2((Z[lfn,1])^ij)(Subscript[((γ^5)), ab])□(OverTilde[A]) +2i ((Z[lfn,2])^ij)(Subscript[C, ab])□ (OverTilde[B]) +2((Z[lfn,3])^ij)(Subscript[((γ^5)(γ^μ)), ab])(∂_μ)(OverTilde[F])+2 i ((Z[lfn,4])^ij)(Subscript[((γ^μ)), ab])(∂_μ)(OverTilde[G])+2 ((Z[lfn,5])^ij)(Subscript[((γ^5)), ab])□φ+ ((Z[lfn,6])^ij)(Subscript[((γ^5)[(γ^α),(γ^β)]), ab])□(Subscript[B, αβ])+((Z[lfn,7])^ij)(Subscript[((γ^5)[(γ^α),(γ^μ)]), ab])(∂_μ)(∂^β)(Subscript[B, αβ]) 
lfn = FieldNumber = 4

LocalField = G[t,x,y,z];
LocalFieldNumber = 4;
CentralChargeList[LocalFieldNumber] = Table[z[LocalFieldNumber,FieldNumber,sigmaNumber],{FieldNumber,1,7},{sigmaNumber,0,3}]//Flatten

Z[LocalFieldNumber][ii_,jj_][aa_,bb_]:=2 ZGen[LocalFieldNumber,1][ii,jj]γ5down[[aa,bb]]Lap[At[t,x,y,z]]+2I ZGen[LocalFieldNumber,2][ii,jj]Cmetric[[aa,bb]]Lap[Bt[t,x,y,z]] + 2ZGen[LocalFieldNumber,3][ii,jj]Sum[γ5γdown[mu][[aa,bb]]D[Ft[t,x,y,z],Ϛ[mu]],{mu,0, 3}]+ 2 I ZGen[LocalFieldNumber,4][ii,jj]Sum[γdown[mu][[aa,bb]]D[Gt[t,x,y,z],Ϛ[mu]],{mu,0, 3}]+2 ZGen[LocalFieldNumber,5][ii,jj]γ5down[[aa,bb]]Lap[φ[t,x,y,z]]+ ZGen[LocalFieldNumber,6][ii,jj]Sum[(γ5.CommuteGammadown[ap,bt])[[aa,bb]]Lap[Bmn[ap,bt][t,x,y,z]],{ap,0,3},{bt,0,3}] + ZGen[LocalFieldNumber,7][ii,jj]Sum[(γ5.CommuteGammadown[ap,mu])[[aa,bb]]D[UD[Bmn[ap,bt][t,x,y,z],Ϛ[bt]],Ϛ[mu]],{ap,0,3},{bt,0,3},{mu,0,3}]

ZTable[LocalFieldNumber] = Table[Z[LocalFieldNumber][ii,jj][aa,bb],{ii,1,2},{aa,1,4},{jj,1,2},{bb,1,4}];

AlgebraDDMinusClosure[tt1,tt2][LocalFieldNumber]=(Collect[(AlgebraDD[tt1,tt2][LocalField] - ZTable[LocalFieldNumber])/.LagrangianParameters/.VtoPauli,FieldListWithDerivatives,Simplify]);

AlgebraDDEqs[tt1,tt2][LocalFieldNumber] = DeleteCases[Table[(Coefficient[AlgebraDDMinusClosure[tt1,tt2][LocalFieldNumber][[ii,aa,jj,bb]],FieldListWithDerivatives[[FieldListIndex]]])==0,{ii,1,2},{aa,1,4},{jj,1,2},{bb,1,4},{FieldListIndex,1,Length[FieldListWithDerivatives]}]//Simplify//Flatten,True]//DeleteDuplicates;

Length[AlgebraDDEqs[tt1,tt2][LocalFieldNumber]]

ZSolutions[LocalFieldNumber] = Solve[AlgebraDDEqs[tt1,tt2][LocalFieldNumber],CentralChargeList[LocalFieldNumber]]//Flatten

ZSolutions[LocalFieldNumber]/.ThisOneLooksGood

{(Subscript[D, a]^i),(Subscript[(OverTilde[D]), b]^j)}G= 2((Z[lfn,1])^ij)(Subscript[((γ^5)), ab])□(OverTilde[A]) +2i ((Z[lfn,2])^ij)(Subscript[C, ab])□ (OverTilde[B]) +2((Z[lfn,3])^ij)(Subscript[((γ^5)(γ^μ)), ab])(∂_μ)(OverTilde[F])+2 i ((Z[lfn,4])^ij)(Subscript[((γ^μ)), ab])(∂_μ)(OverTilde[G])+2 ((Z[lfn,5])^ij)(Subscript[((γ^5)), ab])□φ+ ((Z[lfn,6])^ij)(Subscript[((γ^5)[(γ^α),(γ^β)]), ab])□(Subscript[B, αβ])+((Z[lfn,7])^ij)(Subscript[((γ^5)[(γ^α),(γ^μ)]), ab])(∂_μ)(∂^β)(Subscript[B, αβ]) 
lfn = FieldNumber = 4

DeleteCases[Table[Z[LocalFieldNumber,nn]==PrintSigmaProduct[Table[ZGen[LocalFieldNumber,nn][ii,jj],{ii,1,2},{jj,1,2}]/.ZSolutions[LocalFieldNumber]/.ThisOneLooksGood],{nn,1,7}],Z[_,_]==0]
TeXForm[%]

Clear[LocalField,LocalFieldNumber]

{(Subscript[D, a]^i),(Subscript[(OverTilde[D]), b]^j)}d=  2((Z[lfn,1])^ij)(Subscript[((γ^5)), ab])□(OverTilde[A]) +2i ((Z[lfn,2])^ij)(Subscript[C, ab])□ (OverTilde[B]) +2((Z[lfn,3])^ij)(Subscript[((γ^5)(γ^μ)), ab])(∂_μ)(OverTilde[F])+2 i ((Z[lfn,4])^ij)(Subscript[((γ^μ)), ab])(∂_μ)(OverTilde[G])+2 ((Z[lfn,5])^ij)(Subscript[((γ^5)), ab])□φ+ ((Z[lfn,6])^ij)(Subscript[((γ^5)[(γ^α),(γ^β)]), ab])□(Subscript[B, αβ])+((Z[lfn,7])^ij)(Subscript[((γ^5)[(γ^α),(γ^μ)]), ab])(∂_μ)(∂^β)(Subscript[B, αβ]) 
lfn = FieldNumber = 5

LocalField = d[t,x,y,z];
LocalFieldNumber = 5;
CentralChargeList[LocalFieldNumber] = Table[z[LocalFieldNumber,FieldNumber,sigmaNumber],{FieldNumber,1,7},{sigmaNumber,0,3}]//Flatten

Z[LocalFieldNumber][ii_,jj_][aa_,bb_]:=2 ZGen[LocalFieldNumber,1][ii,jj]γ5down[[aa,bb]]Lap[At[t,x,y,z]]+2I ZGen[LocalFieldNumber,2][ii,jj]Cmetric[[aa,bb]]Lap[Bt[t,x,y,z]] + 2ZGen[LocalFieldNumber,3][ii,jj]Sum[γ5γdown[mu][[aa,bb]]D[Ft[t,x,y,z],Ϛ[mu]],{mu,0, 3}]+ 2 I ZGen[LocalFieldNumber,4][ii,jj]Sum[γdown[mu][[aa,bb]]D[Gt[t,x,y,z],Ϛ[mu]],{mu,0, 3}]+2 ZGen[LocalFieldNumber,5][ii,jj]γ5down[[aa,bb]]Lap[φ[t,x,y,z]]+ ZGen[LocalFieldNumber,6][ii,jj]Sum[(γ5.CommuteGammadown[ap,bt])[[aa,bb]]Lap[Bmn[ap,bt][t,x,y,z]],{ap,0,3},{bt,0,3}] + ZGen[LocalFieldNumber,7][ii,jj]Sum[(γ5.CommuteGammadown[ap,mu])[[aa,bb]]D[UD[Bmn[ap,bt][t,x,y,z],Ϛ[bt]],Ϛ[mu]],{ap,0,3},{bt,0,3},{mu,0,3}]

ZTable[LocalFieldNumber] = Table[Z[LocalFieldNumber][ii,jj][aa,bb],{ii,1,2},{aa,1,4},{jj,1,2},{bb,1,4}];

AlgebraDDMinusClosure[tt1,tt2][LocalFieldNumber]=(Collect[(AlgebraDD[tt1,tt2][LocalField] - ZTable[LocalFieldNumber])/.LagrangianParameters/.VtoPauli,FieldListWithDerivatives,Simplify]);

AlgebraDDEqs[tt1,tt2][LocalFieldNumber] = DeleteCases[Table[(Coefficient[AlgebraDDMinusClosure[tt1,tt2][LocalFieldNumber][[ii,aa,jj,bb]],FieldListWithDerivatives[[FieldListIndex]]])==0,{ii,1,2},{aa,1,4},{jj,1,2},{bb,1,4},{FieldListIndex,1,Length[FieldListWithDerivatives]}]//Simplify//Flatten,True]//DeleteDuplicates;

Length[AlgebraDDEqs[tt1,tt2][LocalFieldNumber]]

ZSolutions[LocalFieldNumber] = Solve[AlgebraDDEqs[tt1,tt2][LocalFieldNumber],CentralChargeList[LocalFieldNumber]]//Flatten

ZSolutions[LocalFieldNumber]/.ThisOneLooksGood

{(Subscript[D, a]^i),(Subscript[(OverTilde[D]), b]^j)}d=  2((Z[lfn,1])^ij)(Subscript[((γ^5)), ab])□(OverTilde[A]) +2i ((Z[lfn,2])^ij)(Subscript[C, ab])□ (OverTilde[B]) +2((Z[lfn,3])^ij)(Subscript[((γ^5)(γ^μ)), ab])(∂_μ)(OverTilde[F])+2 i ((Z[lfn,4])^ij)(Subscript[((γ^μ)), ab])(∂_μ)(OverTilde[G])+2 ((Z[lfn,5])^ij)(Subscript[((γ^5)), ab])□φ+ ((Z[lfn,6])^ij)(Subscript[((γ^5)[(γ^α),(γ^β)]), ab])□(Subscript[B, αβ])+((Z[lfn,7])^ij)(Subscript[((γ^5)[(γ^α),(γ^μ)]), ab])(∂_μ)(∂^β)(Subscript[B, αβ]) 
lfn = FieldNumber = 5

DeleteCases[Table[Z[LocalFieldNumber,nn]==PrintSigmaProduct[Table[ZGen[LocalFieldNumber,nn][ii,jj],{ii,1,2},{jj,1,2}]/.ZSolutions[LocalFieldNumber]/.ThisOneLooksGood],{nn,1,7}],Z[_,_]==0]

Clear[LocalField,LocalFieldNumber]

{(Subscript[D, a]^i),(Subscript[(OverTilde[D]), b]^j)}At= 2i ((Z[lfn,1])^ij)(Subscript[((γ^μ)), ab])(∂_μ)A +2((Z[lfn,2])^ij)(Subscript[((γ^5)(γ^μ)), ab])(∂_μ)B +2i ((Z[lfn,3])^ij)(Subscript[C, ab])F+2 ((Z[lfn,4])^ij)(Subscript[((γ^5)), ab])G+2 ((Z[lfn,5])^ij)(Subscript[((γ^5)), ab])d +i ((Z[lfn,6])^ij)(Subscript[C, ab])(∂^μ)(Subscript[A, μ])+i ((Z[lfn,7])^ij)(Subscript[([(γ^μ),(γ^ν)]), ab])(∂_μ)(Subscript[A, ν])  
lfn = FieldNumber = 8

LocalField = At[t,x,y,z];
LocalFieldNumber = 8;
CentralChargeList[LocalFieldNumber] = Table[z[LocalFieldNumber,FieldNumber,sigmaNumber],{FieldNumber,1,7},{sigmaNumber,0,3}]//Flatten

Z[LocalFieldNumber][ii_,jj_][aa_,bb_]:=2 I ZGen[LocalFieldNumber,1][ii,jj]Sum[γdown[mu][[aa,bb]]D[A[t,x,y,z],Ϛ[mu]],{mu,0,3}]+2 ZGen[LocalFieldNumber,2][ii,jj]Sum[γ5γdown[mu][[aa,bb]]D[B[t,x,y,z],Ϛ[mu]],{mu,0,3}] + 2 I ZGen[LocalFieldNumber,3][ii,jj]Cmetric[[aa,bb]]F[t,x,y,z]+ 2 ZGen[LocalFieldNumber,4][ii,jj]γ5down[[aa,bb]]G[t,x,y,z]+ 2 ZGen[LocalFieldNumber,5][ii,jj]γ5down[[aa,bb]]d[t,x,y,z] +I ZGen[LocalFieldNumber,6][ii,jj]Cmetric[[aa,bb]]Sum[UD[Am[mu][t,x,y,z],Ϛ[mu]],{mu,0,3}]+I ZGen[LocalFieldNumber,7][ii,jj]Sum[CommuteGammadown[mu,nu][[aa,bb]]D[Am[nu][t,x,y,z],Ϛ[mu]],{mu,0,3},{nu,0,3}]

ZTable[LocalFieldNumber] = Table[Z[LocalFieldNumber][ii,jj][aa,bb],{ii,1,2},{aa,1,4},{jj,1,2},{bb,1,4}];

AlgebraDDMinusClosure[tt1,tt2][LocalFieldNumber]=(Collect[(AlgebraDD[tt1,tt2][LocalField] - ZTable[LocalFieldNumber])/.LagrangianParameters/.VtoPauli,FieldListWithDerivatives,Simplify]);

AlgebraDDEqs[tt1,tt2][LocalFieldNumber] = DeleteCases[Table[(Coefficient[AlgebraDDMinusClosure[tt1,tt2][LocalFieldNumber][[ii,aa,jj,bb]],FieldListWithDerivatives[[FieldListIndex]]])==0,{ii,1,2},{aa,1,4},{jj,1,2},{bb,1,4},{FieldListIndex,1,Length[FieldListWithDerivatives]}]//Simplify//Flatten,True]//DeleteDuplicates;

Length[AlgebraDDEqs[tt1,tt2][LocalFieldNumber]]

ZSolutions[LocalFieldNumber] = Solve[AlgebraDDEqs[tt1,tt2][LocalFieldNumber],CentralChargeList[LocalFieldNumber]]//Flatten

{(Subscript[D, a]^i),(Subscript[(OverTilde[D]), b]^j)}At= 2i ((Z[lfn,1])^ij)(Subscript[((γ^μ)), ab])(∂_μ)A +2((Z[lfn,2])^ij)(Subscript[((γ^5)(γ^μ)), ab])(∂_μ)B +2i ((Z[lfn,3])^ij)(Subscript[C, ab])F+2 ((Z[lfn,4])^ij)(Subscript[((γ^5)), ab])G+2 ((Z[lfn,5])^ij)(Subscript[((γ^5)), ab])d +i ((Z[lfn,6])^ij)(Subscript[C, ab])(∂^μ)(Subscript[A, μ])+i ((Z[lfn,7])^ij)(Subscript[([(γ^μ),(γ^ν)]), ab])(∂_μ)(Subscript[A, ν])  
lfn = FieldNumber = 8

DeleteCases[Table[Z[LocalFieldNumber,nn]==PrintSigmaProduct[Table[ZGen[LocalFieldNumber,nn][ii,jj],{ii,1,2},{jj,1,2}]/.ZSolutions[LocalFieldNumber]/.ThisOneLooksGood],{nn,1,7}],Z[_,_]==0]

Clear[LocalField,LocalFieldNumber]

{(Subscript[D, a]^i),(Subscript[(OverTilde[D]), b]^j)}Bt=2 ((Z[lfn,1])^ij)(Subscript[((γ^5)(γ^μ)), ab])(∂_μ)A +2i ((Z[lfn,2])^ij)(Subscript[((γ^μ)), ab])(∂_μ)B +2((Z[lfn,3])^ij)(Subscript[((γ^5)), ab])F+2 i ((Z[lfn,4])^ij)(Subscript[C, ab])G+2 i ((Z[lfn,5])^ij)(Subscript[C, ab])d +((Z[lfn,6])^ij)(Subscript[((γ^5)), ab])(∂^μ)(Subscript[A, μ])+((Z[lfn,7])^ij)(Subscript[((γ^5)[(γ^μ),(γ^ν)]), ab])(∂_μ)(Subscript[A, ν]) 
lfn = FieldNumber = 9

LocalField = Bt[t,x,y,z];
LocalFieldNumber = 9;
CentralChargeList[LocalFieldNumber] = Table[z[LocalFieldNumber,FieldNumber,sigmaNumber],{FieldNumber,1,7},{sigmaNumber,0,3}]//Flatten

Z[LocalFieldNumber][ii_,jj_][aa_,bb_]:=2 ZGen[LocalFieldNumber,1][ii,jj]Sum[γ5γdown[mu][[aa,bb]]D[A[t,x,y,z],Ϛ[mu]],{mu,0,3}]+2 I ZGen[LocalFieldNumber,2][ii,jj]Sum[γdown[mu][[aa,bb]]D[B[t,x,y,z],Ϛ[mu]],{mu,0,3}] + 2 ZGen[LocalFieldNumber,3][ii,jj]γ5down[[aa,bb]]F[t,x,y,z]+ 2 I ZGen[LocalFieldNumber,4][ii,jj]Cmetric[[aa,bb]]G[t,x,y,z]+ 2 I ZGen[LocalFieldNumber,5][ii,jj]Cmetric[[aa,bb]]d[t,x,y,z] +ZGen[LocalFieldNumber,6][ii,jj]γ5down[[aa,bb]]Sum[UD[Am[mu][t,x,y,z],Ϛ[mu]],{mu,0,3}]+ZGen[LocalFieldNumber,7][ii,jj]Sum[(γ5.CommuteGammadown[mu,nu])[[aa,bb]]D[Am[nu][t,x,y,z],Ϛ[mu]],{mu,0,3},{nu,0,3}]

ZTable[LocalFieldNumber] = Table[Z[LocalFieldNumber][ii,jj][aa,bb],{ii,1,2},{aa,1,4},{jj,1,2},{bb,1,4}];

AlgebraDDMinusClosure[tt1,tt2][LocalFieldNumber]=(Collect[(AlgebraDD[tt1,tt2][LocalField] - ZTable[LocalFieldNumber])/.LagrangianParameters/.VtoPauli,FieldListWithDerivatives,Simplify]);

AlgebraDDEqs[tt1,tt2][LocalFieldNumber] = DeleteCases[Table[(Coefficient[AlgebraDDMinusClosure[tt1,tt2][LocalFieldNumber][[ii,aa,jj,bb]],FieldListWithDerivatives[[FieldListIndex]]])==0,{ii,1,2},{aa,1,4},{jj,1,2},{bb,1,4},{FieldListIndex,1,Length[FieldListWithDerivatives]}]//Simplify//Flatten,True]//DeleteDuplicates;

Length[AlgebraDDEqs[tt1,tt2][LocalFieldNumber]]

ZSolutions[LocalFieldNumber] = Solve[AlgebraDDEqs[tt1,tt2][LocalFieldNumber],CentralChargeList[LocalFieldNumber]]//Flatten

ZSolutions[LocalFieldNumber]/.ThisOneLooksGood

{(Subscript[D, a]^i),(Subscript[(OverTilde[D]), b]^j)}Bt=2 ((Z[lfn,1])^ij)(Subscript[((γ^5)(γ^μ)), ab])(∂_μ)A +2i ((Z[lfn,2])^ij)(Subscript[((γ^μ)), ab])(∂_μ)B +2((Z[lfn,3])^ij)(Subscript[((γ^5)), ab])F+2 i ((Z[lfn,4])^ij)(Subscript[C, ab])G+2 i ((Z[lfn,5])^ij)(Subscript[C, ab])d +((Z[lfn,6])^ij)(Subscript[((γ^5)), ab])(∂^μ)(Subscript[A, μ])+((Z[lfn,7])^ij)(Subscript[((γ^5)[(γ^μ),(γ^ν)]), ab])(∂_μ)(Subscript[A, ν]) 
lfn = FieldNumber = 9

DeleteCases[Table[Z[LocalFieldNumber,nn]==PrintSigmaProduct[Table[ZGen[LocalFieldNumber,nn][ii,jj],{ii,1,2},{jj,1,2}]/.ZSolutions[LocalFieldNumber]/.ThisOneLooksGood],{nn,1,7}],Z[_,_]==0]

Clear[LocalField,LocalFieldNumber]

{(Subscript[D, a]^i),(Subscript[(OverTilde[D]), b]^j)}Ft= 2i ((Z[lfn,1])^ij)(Subscript[C, ab])□A +2((Z[lfn,2])^ij)(Subscript[((γ^5)), ab])□ B +2((iZ[lfn,3])^ij)(Subscript[((γ^μ)), ab])(∂_μ)F+2 ((Z[lfn,4])^ij)(Subscript[((γ^5)(γ^μ)), ab])(∂_μ)G+2 ((Z[lfn,5])^ij)(Subscript[((γ^5)(γ^μ)), ab])(∂_μ)d +i ((Z[lfn,6])^ij)(Subscript[((γ^μ)), ab])□(Subscript[A, μ])+i ((Z[lfn,7])^ij)(Subscript[((γ^μ)), ab])(∂_μ)(∂^ν)(Subscript[A, ν]) 
FieldNumber = 10

LocalField = Ft[t,x,y,z];
LocalFieldNumber = 10;
CentralChargeList[LocalFieldNumber] = Table[z[LocalFieldNumber,FieldNumber,sigmaNumber],{FieldNumber,1,7},{sigmaNumber,0,3}]//Flatten

Z[LocalFieldNumber][ii_,jj_][aa_,bb_]:=2 I ZGen[LocalFieldNumber,1][ii,jj]Cmetric[[aa,bb]]Lap[A[t,x,y,z]]+2 ZGen[LocalFieldNumber,2][ii,jj]γ5down[[aa,bb]]Lap[B[t,x,y,z]] + 2 I ZGen[LocalFieldNumber,3][ii,jj]Sum[γdown[mu][[aa,bb]]D[F[t,x,y,z],Ϛ[mu]],{mu,0, 3}]+ 2 ZGen[LocalFieldNumber,4][ii,jj]Sum[γ5γdown[mu][[aa,bb]]D[G[t,x,y,z],Ϛ[mu]],{mu,0, 3}]+ 2 ZGen[LocalFieldNumber,5][ii,jj]Sum[γ5γdown[mu][[aa,bb]]D[d[t,x,y,z],Ϛ[mu]],{mu,0, 3}]+I ZGen[LocalFieldNumber,6][ii,jj]Sum[γdown[mu][[aa,bb]]Lap[Am[mu][t,x,y,z]],{mu,0,3}] + I ZGen[LocalFieldNumber,7][ii,jj]Sum[γdown[mu][[aa,bb]]D[UD[Am[nu][t,x,y,z],Ϛ[nu]],Ϛ[mu]],{mu,0,3},{nu,0,3}]

ZTable[LocalFieldNumber] = Table[Z[LocalFieldNumber][ii,jj][aa,bb],{ii,1,2},{aa,1,4},{jj,1,2},{bb,1,4}];

AlgebraDDMinusClosure[tt1,tt2][LocalFieldNumber]=(Collect[(AlgebraDD[tt1,tt2][LocalField] - ZTable[LocalFieldNumber])/.LagrangianParameters/.VtoPauli,FieldListWithDerivatives,Simplify]);

AlgebraDDEqs[tt1,tt2][LocalFieldNumber] = DeleteCases[Table[(Coefficient[AlgebraDDMinusClosure[tt1,tt2][LocalFieldNumber][[ii,aa,jj,bb]],FieldListWithDerivatives[[FieldListIndex]]])==0,{ii,1,2},{aa,1,4},{jj,1,2},{bb,1,4},{FieldListIndex,1,Length[FieldListWithDerivatives]}]//Simplify//Flatten,True]//DeleteDuplicates;

Length[AlgebraDDEqs[tt1,tt2][LocalFieldNumber]]

ZSolutions[LocalFieldNumber] = Solve[AlgebraDDEqs[tt1,tt2][LocalFieldNumber],CentralChargeList[LocalFieldNumber]]//Flatten

ZSolutions[LocalFieldNumber]/.ThisOneLooksGood

{(Subscript[D, a]^i),(Subscript[(OverTilde[D]), b]^j)}Ft= 2i ((Z[lfn,1])^ij)(Subscript[C, ab])□A +2((Z[lfn,2])^ij)(Subscript[((γ^5)), ab])□ B +2((iZ[lfn,3])^ij)(Subscript[((γ^μ)), ab])(∂_μ)F+2 ((Z[lfn,4])^ij)(Subscript[((γ^5)(γ^μ)), ab])(∂_μ)G+2 ((Z[lfn,5])^ij)(Subscript[((γ^5)(γ^μ)), ab])(∂_μ)d +i ((Z[lfn,6])^ij)(Subscript[((γ^μ)), ab])□(Subscript[A, μ])+i ((Z[lfn,7])^ij)(Subscript[((γ^μ)), ab])(∂_μ)(∂^ν)(Subscript[A, ν]) 
FieldNumber = 10

DeleteCases[Table[Z[LocalFieldNumber,nn]==PrintSigmaProduct[Table[ZGen[LocalFieldNumber,nn][ii,jj],{ii,1,2},{jj,1,2}]/.ZSolutions[LocalFieldNumber]/.ThisOneLooksGood],{nn,1,7}],Z[_,_]==0]

Clear[LocalField,LocalFieldNumber]

{(Subscript[D, a]^i),(Subscript[(OverTilde[D]), b]^j)}Gt= 2((Z[lfn,1])^ij)(Subscript[((γ^5)), ab])□A +2i ((Z[lfn,2])^ij)(Subscript[C, ab])□ B +2((Z[lfn,3])^ij)(Subscript[((γ^5)(γ^μ)), ab])(∂_μ)F+2 i ((Z[lfn,4])^ij)(Subscript[((γ^μ)), ab])(∂_μ)G+2 i ((Z[lfn,5])^ij)(Subscript[((γ^μ)), ab])(∂_μ)d +((Z[lfn,6])^ij)(Subscript[((γ^5)(γ^μ)), ab])□(Subscript[A, μ])+((Z[lfn,7])^ij)(Subscript[((γ^5)(γ^μ)), ab])(∂_μ)(∂^ν)(Subscript[A, ν])
FieldNumber = 11

LocalField = Gt[t,x,y,z];
LocalFieldNumber = 11;
CentralChargeList[LocalFieldNumber] = Table[z[LocalFieldNumber,FieldNumber,sigmaNumber],{FieldNumber,1,7},{sigmaNumber,0,3}]//Flatten

Z[LocalFieldNumber][ii_,jj_][aa_,bb_]:=2 ZGen[LocalFieldNumber,1][ii,jj]γ5down[[aa,bb]]Lap[A[t,x,y,z]]+2I ZGen[LocalFieldNumber,2][ii,jj]Cmetric[[aa,bb]]Lap[B[t,x,y,z]] + 2ZGen[LocalFieldNumber,3][ii,jj]Sum[γ5γdown[mu][[aa,bb]]D[F[t,x,y,z],Ϛ[mu]],{mu,0, 3}]+ 2 I ZGen[LocalFieldNumber,4][ii,jj]Sum[γdown[mu][[aa,bb]]D[G[t,x,y,z],Ϛ[mu]],{mu,0, 3}]+2 I ZGen[LocalFieldNumber,5][ii,jj]Sum[γdown[mu][[aa,bb]]D[d[t,x,y,z],Ϛ[mu]],{mu,0, 3}]+ ZGen[LocalFieldNumber,6][ii,jj]Sum[γ5γdown[mu][[aa,bb]]Lap[Am[mu][t,x,y,z]],{mu,0,3}] + ZGen[LocalFieldNumber,7][ii,jj]Sum[γ5γdown[mu][[aa,bb]]D[UD[Am[nu][t,x,y,z],Ϛ[nu]],Ϛ[mu]],{mu,0,3},{nu,0,3}]

ZTable[LocalFieldNumber] = Table[Z[LocalFieldNumber][ii,jj][aa,bb],{ii,1,2},{aa,1,4},{jj,1,2},{bb,1,4}];

AlgebraDDMinusClosure[tt1,tt2][LocalFieldNumber]=(Collect[(AlgebraDD[tt1,tt2][LocalField] - ZTable[LocalFieldNumber])/.LagrangianParameters/.VtoPauli,FieldListWithDerivatives,Simplify]);

AlgebraDDEqs[tt1,tt2][LocalFieldNumber] = DeleteCases[Table[(Coefficient[AlgebraDDMinusClosure[tt1,tt2][LocalFieldNumber][[ii,aa,jj,bb]],FieldListWithDerivatives[[FieldListIndex]]])==0,{ii,1,2},{aa,1,4},{jj,1,2},{bb,1,4},{FieldListIndex,1,Length[FieldListWithDerivatives]}]//Simplify//Flatten,True]//DeleteDuplicates;

Length[AlgebraDDEqs[tt1,tt2][LocalFieldNumber]]

ZSolutions[LocalFieldNumber] = Solve[AlgebraDDEqs[tt1,tt2][LocalFieldNumber],CentralChargeList[LocalFieldNumber]]//Flatten

ZSolutions[LocalFieldNumber]/.ThisOneLooksGood

{(Subscript[D, a]^i),(Subscript[(OverTilde[D]), b]^j)}Gt= 2((Z[lfn,1])^ij)(Subscript[((γ^5)), ab])□A +2i ((Z[lfn,2])^ij)(Subscript[C, ab])□ B +2((Z[lfn,3])^ij)(Subscript[((γ^5)(γ^μ)), ab])(∂_μ)F+2 i ((Z[lfn,4])^ij)(Subscript[((γ^μ)), ab])(∂_μ)G+2 i ((Z[lfn,5])^ij)(Subscript[((γ^μ)), ab])(∂_μ)d +((Z[lfn,6])^ij)(Subscript[((γ^5)(γ^μ)), ab])□(Subscript[A, μ])+((Z[lfn,7])^ij)(Subscript[((γ^5)(γ^μ)), ab])(∂_μ)(∂^ν)(Subscript[A, ν])
FieldNumber = 11

DeleteCases[Table[Z[LocalFieldNumber,nn]==PrintSigmaProduct[Table[ZGen[LocalFieldNumber,nn][ii,jj],{ii,1,2},{jj,1,2}]/.ZSolutions[LocalFieldNumber]/.ThisOneLooksGood],{nn,1,7}],Z[_,_]==0]

Clear[LocalField,LocalFieldNumber]

{(Subscript[D, a]^i),(Subscript[(OverTilde[D]), b]^j)}φ= 2i ((Z[lfn,1])^ij)(Subscript[((γ^μ)), ab])(∂_μ)A +2((Z[lfn,2])^ij)(Subscript[((γ^5)(γ^μ)), ab])(∂_μ)B +2i ((Z[lfn,3])^ij)(Subscript[C, ab])F+2 ((Z[lfn,4])^ij)(Subscript[((γ^5)), ab])G+2 ((Z[lfn,5])^ij)(Subscript[((γ^5)), ab])d +i ((Z[lfn,6])^ij)(Subscript[C, ab])(∂^μ)(Subscript[A, μ])+i ((Z[lfn,7])^ij)(Subscript[([(γ^μ),(γ^ν)]), ab])(∂_μ)(Subscript[A, ν]) 
FieldNumber = 12

LocalField = φ[t,x,y,z];
LocalFieldNumber = 12;
CentralChargeList[LocalFieldNumber] = Table[z[LocalFieldNumber,FieldNumber,sigmaNumber],{FieldNumber,1,7},{sigmaNumber,0,3}]//Flatten

Z[LocalFieldNumber][ii_,jj_][aa_,bb_]:=2 I ZGen[LocalFieldNumber,1][ii,jj]Sum[γdown[mu][[aa,bb]]D[A[t,x,y,z],Ϛ[mu]],{mu,0,3}]+2 ZGen[LocalFieldNumber,2][ii,jj]Sum[γ5γdown[mu][[aa,bb]]D[B[t,x,y,z],Ϛ[mu]],{mu,0,3}] + 2 I ZGen[LocalFieldNumber,3][ii,jj]Cmetric[[aa,bb]]F[t,x,y,z]+ 2 ZGen[LocalFieldNumber,4][ii,jj]γ5down[[aa,bb]]G[t,x,y,z]+ 2 ZGen[LocalFieldNumber,5][ii,jj]γ5down[[aa,bb]]d[t,x,y,z] +I ZGen[LocalFieldNumber,6][ii,jj]Cmetric[[aa,bb]]Sum[UD[Am[mu][t,x,y,z],Ϛ[mu]],{mu,0,3}]+I ZGen[LocalFieldNumber,7][ii,jj]Sum[CommuteGammadown[mu,nu][[aa,bb]]D[Am[nu][t,x,y,z],Ϛ[mu]],{mu,0,3},{nu,0,3}]

ZTable[LocalFieldNumber] = Table[Z[LocalFieldNumber][ii,jj][aa,bb],{ii,1,2},{aa,1,4},{jj,1,2},{bb,1,4}];

AlgebraDDMinusClosure[tt1,tt2][LocalFieldNumber]=(Collect[(AlgebraDD[tt1,tt2][LocalField] - ZTable[LocalFieldNumber])/.LagrangianParameters/.VtoPauli,FieldListWithDerivatives,Simplify]);

AlgebraDDEqs[tt1,tt2][LocalFieldNumber] = DeleteCases[Table[(Coefficient[AlgebraDDMinusClosure[tt1,tt2][LocalFieldNumber][[ii,aa,jj,bb]],FieldListWithDerivatives[[FieldListIndex]]])==0,{ii,1,2},{aa,1,4},{jj,1,2},{bb,1,4},{FieldListIndex,1,Length[FieldListWithDerivatives]}]//Simplify//Flatten,True]//DeleteDuplicates;

Length[AlgebraDDEqs[tt1,tt2][LocalFieldNumber]]

ZSolutions[LocalFieldNumber] = Solve[AlgebraDDEqs[tt1,tt2][LocalFieldNumber],CentralChargeList[LocalFieldNumber]]//Flatten

{(Subscript[D, a]^i),(Subscript[(OverTilde[D]), b]^j)}φ= 2i ((Z[lfn,1])^ij)(Subscript[((γ^μ)), ab])(∂_μ)A +2((Z[lfn,2])^ij)(Subscript[((γ^5)(γ^μ)), ab])(∂_μ)B +2i ((Z[lfn,3])^ij)(Subscript[C, ab])F+2 ((Z[lfn,4])^ij)(Subscript[((γ^5)), ab])G+2 ((Z[lfn,5])^ij)(Subscript[((γ^5)), ab])d +i ((Z[lfn,6])^ij)(Subscript[C, ab])(∂^μ)(Subscript[A, μ])+i ((Z[lfn,7])^ij)(Subscript[([(γ^μ),(γ^ν)]), ab])(∂_μ)(Subscript[A, ν]) 
FieldNumber = 12

DeleteCases[Table[Z[LocalFieldNumber,nn]==PrintSigmaProduct[Table[ZGen[LocalFieldNumber,nn][ii,jj],{ii,1,2},{jj,1,2}]/.ZSolutions[LocalFieldNumber]/.ThisOneLooksGood],{nn,1,7}],Z[_,_]==0]

Clear[LocalField,LocalFieldNumber]

{(Subscript[D, a]^i),(Subscript[(OverTilde[D]), b]^j)}(Subscript[A, μ])=2 i ((Z[lfn,1])^ij)(Subscript[([(Subscript[γ, μ]),(Subscript[γ, ν])]), ab])(∂^ν)At +2 ((Z[lfn,2])^ij)(Subscript[((γ^5)[(Subscript[γ, μ]),(Subscript[γ, ν])]), ab])(∂^ν)Bt +2 i ((Z[lfn,3])^ij)(Subscript[((Subscript[γ, μ])), ab])Ft +2 ((Z[lfn,4])^ij)(Subscript[((γ^5)(Subscript[γ, μ])), ab])Gt +2 i ((Z[lfn,5])^ij)(Subscript[([(Subscript[γ, μ]),(Subscript[γ, ν])]), ab])(∂^ν)φ +i ((Z[lfn,6])^ij)(Subscript[C, ab])(∂^α)(Subscript[B, αμ])+i ((Z[lfn,7])^ij)(Subscript[([(γ^α),(γ^β)]), ab])(∂_α)(Subscript[B, βμ]) + ((Z[lfn,8])^ij) (Subscript[((γ^5)), ab]) (Subscript[ϵ, μναβ])(∂^ν)(B^(αβ))-(∂_μ)(Subscript[(OverTilde[λ]), ab]^ij)  ,
FieldNumber = 7
(Subscript[(OverTilde[λ]), ab]^ij)= i ((Z[lfn,9])^ij)(Subscript[([(γ^α),(γ^β)]), ab])(Subscript[B, αβ]) + 2i ((Z[lfn,10])^ij)(Subscript[C, ab])(OverTilde[A]) 
+ 2 ((Z[lfn,11])^ij) (Subscript[((γ^5)), ab])(OverTilde[B])+ 2i ((Z[lfn,12])^ij)(Subscript[C, ab])φ
The Z[9] through Z[12] are actually gauge charges

LocalFieldNumber = 7;
NumZCharges = 12;
CentralChargeList[LocalFieldNumber] = Table[z[LocalFieldNumber,FieldNumber,sigmaNumber],{FieldNumber,1,NumZCharges},{sigmaNumber,0,3}]//Flatten

Z[LocalFieldNumber][mu_][ii_,jj_][aa_,bb_]:=2 I ZGen[LocalFieldNumber,1][ii,jj]Sum[CommuteGammastdowndown[mu,nu][[aa,bb]]UD[At[t,x,y,z],Ϛ[nu]],{nu,0,3}] + 2 ZGen[LocalFieldNumber,2][ii,jj]Sum[(γ5.CommuteGammastdowndown[mu,nu])[[aa,bb]]UD[Bt[t,x,y,z],Ϛ[nu]],{nu,0,3}]  +2 I ZGen[LocalFieldNumber,3][ii,jj]γstdowndown[mu][[aa,bb]]Ft[t,x,y,z]+ 2 ZGen[LocalFieldNumber,4][ii,jj]γ5γstdowndown[mu][[aa,bb]]Gt[t,x,y,z] + 2 I ZGen[LocalFieldNumber,5][ii,jj]Sum[CommuteGammastdowndown[mu,nu][[aa,bb]]UD[φ[t,x,y,z],Ϛ[nu]],{nu,0,3}] + I ZGen[LocalFieldNumber,6][ii,jj]Cmetric[[aa,bb]]Sum[UD[Bmn[ap,mu][t,x,y,z],Ϛ[ap]],{ap,0,3}]+I ZGen[LocalFieldNumber,7][ii,jj]Sum[CommuteGammadown[ap,bt][[aa,bb]]D[Bmn[bt,mu][t,x,y,z],Ϛ[ap]],{ap,0,3},{bt,0,3}]+ZGen[LocalFieldNumber,8][ii,jj]γ5down[[aa,bb]]Sum[ϵ[mu,nu,ap,bt]UD[Bmnup[ap,bt][t,x,y,z],Ϛ[nu]],{nu,0,3},{ap,0,3},{bt,0,3}]

Do[ZTable[LocalFieldNumber][mu] = Table[Z[LocalFieldNumber][mu][ii,jj][aa,bb],{ii,1,2},{aa,1,4},{jj,1,2},{bb,1,4}],{mu,0,3}];

λ[tt1,tt2][ii_,jj_][aa_,bb_][t,x,y,z] := I ZGen[LocalFieldNumber,9][ii,jj]Sum[CommuteGammadown[ap,bt][[aa,bb]]Bmn[ap,bt][t,x,y,z],{ap,0,3},{bt,0,3}] + 2I  ZGen[LocalFieldNumber,10][ii,jj]Cmetric[[aa,bb]] At[t,x,y,z]  + 2 ZGen[LocalFieldNumber,11][ii,jj]γ5down[[aa,bb]] Bt[t,x,y,z]+ 2I  ZGen[LocalFieldNumber,12][ii,jj]Cmetric[[aa,bb]]φ[t,x,y,z]

λTable[tt1,tt2][t,x,y,z] = Table[λ[tt1,tt2][ii,jj][aa,bb][t,x,y,z],{ii,1,2},{aa,1,4},{jj,1,2},{bb,1,4}];

AlgebraDDMinusClosure[tt1,tt2][LocalFieldNumber]=Table[(Collect[(AlgebraDD[tt1,tt2][Am[mu][t,x,y,z]] - (ZTable[LocalFieldNumber][mu]-D[λTable[tt1,tt2][t,x,y,z],Ϛ[mu]]))/.LagrangianParameters/.VtoPauli,FieldListWithDerivatives,Simplify]),{mu,0,3}];

AlgebraDDEqs[tt1,tt2][LocalFieldNumber] = DeleteCases[Table[(Coefficient[AlgebraDDMinusClosure[tt1,tt2][LocalFieldNumber][[mu,ii,aa,jj,bb]],FieldListWithDerivatives[[FieldListIndex]]])==0,{mu,1,4},{ii,1,2},{aa,1,4},{jj,1,2},{bb,1,4},{FieldListIndex,1,Length[FieldListWithDerivatives]}]//Simplify//Flatten,True]//DeleteDuplicates;

Length[AlgebraDDEqs[tt1,tt2][LocalFieldNumber]]

ZSolutions[LocalFieldNumber] = Solve[AlgebraDDEqs[tt1,tt2][LocalFieldNumber],CentralChargeList[LocalFieldNumber]]//Flatten

{(Subscript[D, a]^i),(Subscript[(OverTilde[D]), b]^j)}(Subscript[A, μ])=2 i ((Z[lfn,1])^ij)(Subscript[([(Subscript[γ, μ]),(Subscript[γ, ν])]), ab])(∂^ν)At +2 ((Z[lfn,2])^ij)(Subscript[((γ^5)[(Subscript[γ, μ]),(Subscript[γ, ν])]), ab])(∂^ν)Bt +2 i ((Z[lfn,3])^ij)(Subscript[((Subscript[γ, μ])), ab])Ft +2 ((Z[lfn,4])^ij)(Subscript[((γ^5)(Subscript[γ, μ])), ab])Gt +2 i ((Z[lfn,5])^ij)(Subscript[([(Subscript[γ, μ]),(Subscript[γ, ν])]), ab])(∂^ν)φ +i ((Z[lfn,6])^ij)(Subscript[C, ab])(∂^α)(Subscript[B, αμ])+i ((Z[lfn,7])^ij)(Subscript[([(γ^α),(γ^β)]), ab])(∂_α)(Subscript[B, βμ]) + ((Z[lfn,8])^ij) (Subscript[((γ^5)), ab]) (Subscript[ϵ, μναβ])(∂^ν)(B^(αβ))-(∂_μ)(Subscript[(OverTilde[λ]), ab]^ij)  ,
FieldNumber = 7
(Subscript[(OverTilde[λ]), ab]^ij)= i ((Z[lfn,9])^ij)(Subscript[([(γ^α),(γ^β)]), ab])(Subscript[B, αβ]) + 2i ((Z[lfn,10])^ij)(Subscript[C, ab])(OverTilde[A]) 
+ 2 ((Z[lfn,11])^ij) (Subscript[((γ^5)), ab])(OverTilde[B])+ 2i ((Z[lfn,12])^ij)(Subscript[C, ab])φ
The Z[9] through Z[12] are actually gauge charges

DeleteCases[Table[Z[LocalFieldNumber,nn]==PrintSigmaProduct[Table[ZGen[LocalFieldNumber,nn][ii,jj],{ii,1,2},{jj,1,2}]/.ZSolutions[LocalFieldNumber]/.ThisOneLooksGood],{nn,1,NumZCharges}],Z[_,_]==0]

Clear[LocalFieldNumber,NumZCharges]

{(Subscript[D, a]^i),(Subscript[(OverTilde[D]), b]^j)}(Subscript[B, μν])=  2 i ((Z[lfn,1])^ij)(Subscript[([(Subscript[γ, μ]),(Subscript[γ, ν])](γ^α)), ab])(∂_α)A+2 i ((Z[lfn,2])^ij)(Subscript[((γ^α)[(Subscript[γ, μ]),(Subscript[γ, ν])]), ab])(∂_α)A 
+ 2 ((Z[lfn,3])^ij)(Subscript[((γ^5)[(Subscript[γ, μ]),(Subscript[γ, ν])](γ^α)), ab])(∂_α)B+2 ((Z[lfn,4])^ij)(Subscript[((γ^5)(γ^α)[(Subscript[γ, μ]),(Subscript[γ, ν])]), ab])(∂_α)B+ 2 i ((Z[lfn,5])^ij)(Subscript[([(Subscript[γ, μ]),(Subscript[γ, ν])]), ab])F+ 2 ((Z[lfn,6])^ij)(Subscript[((γ^5)[(Subscript[γ, μ]),(Subscript[γ, ν])]), ab])G+ 2 ((Z[lfn,7])^ij)(Subscript[((γ^5)[(Subscript[γ, μ]),(Subscript[γ, ν])]), ab])d+((Z[lfn,8])^ij)(Subscript[((γ^5)), ab])(Subscript[ϵ, μναβ])(∂^α)(A^β)+i ((Z[lfn,9])^ij)(Subscript[([(Subscript[γ, μ]),(Subscript[γ, ν])]), ab])(∂^α)(Subscript[A, α])+i ((Z[lfn,10])^ij)(Subscript[([(Subscript[γ, α]),(Subscript[γ, [μ])]), |ab|])(∂^α)(Subscript[A, ν]])-(∂_([μ))(Subscript[(OverTilde[Λ]), ν]ab]^ij)
FieldNumber = 14
(Subscript[(OverTilde[Λ]), νab]^ij)= 2i ((Z[lfn,11])^ij)(Subscript[C, ab])(Subscript[A, ν])+ i (Subscript[((Z[lfn,12])^ij)[(Subscript[γ, ν]),(Subscript[γ, α])], ab])(A^α) 
+i ((Z[lfn,13])^ij)(Subscript[((Subscript[γ, ν])), ab])A + ((Z[lfn,14])^ij)(Subscript[((γ^5)(Subscript[γ, ν])), ab])B 
The Z[11] through Z[14] are actually gauge charges

Amup[μ][t,x,y,z]  = (A^μ), forgot this one

Do[Amup[μ][t,x,y,z] = RaiseSTIndex[AmHolder[μ][t,x,y,z]]/.AmHolder->Am,{μ,0,3}]

Table[Amup[mu][t,x,y,z],{mu,0,3}]//MatrixForm

LocalFieldNumber = 14;
NumZCharges = 14;
CentralChargeList[LocalFieldNumber] = Table[z[LocalFieldNumber,FieldNumber,sigmaNumber],{FieldNumber,1,NumZCharges},{sigmaNumber,0,3}]//Flatten

Z[LocalFieldNumber][mu_,nu_][ii_,jj_][aa_,bb_]:=2 I ZGen[LocalFieldNumber,1][ii,jj]Sum[(CommuteGammastdown[mu,nu].γdown[ap])[[aa,bb]]D[A[t,x,y,z],Ϛ[ap]],{ap,0,3}]+2 I ZGen[LocalFieldNumber,2][ii,jj]Sum[(γ[ap].CommuteGammastdowndown[mu,nu])[[aa,bb]]D[A[t,x,y,z],Ϛ[ap]],{ap,0,3}]+2 ZGen[LocalFieldNumber,3][ii,jj]Sum[(γ5.CommuteGammastdown[mu,nu].γdown[ap])[[aa,bb]]D[B[t,x,y,z],Ϛ[ap]],{ap,0,3}]+2 ZGen[LocalFieldNumber,4][ii,jj]Sum[(γ5γ[ap].CommuteGammastdowndown[mu,nu])[[aa,bb]]D[B[t,x,y,z],Ϛ[ap]],{ap,0,3}] + 2I ZGen[LocalFieldNumber,5][ii,jj]CommuteGammastdowndown[mu,nu][[aa,bb]]F[t,x,y,z] + 2ZGen[LocalFieldNumber,6][ii,jj](γ5.CommuteGammastdowndown[mu,nu])[[aa,bb]]G[t,x,y,z]+ 2ZGen[LocalFieldNumber,7][ii,jj](γ5.CommuteGammastdowndown[mu,nu])[[aa,bb]]d[t,x,y,z]+ZGen[LocalFieldNumber,8][ii,jj]γ5down[[aa,bb]]Sum[ϵ[mu,nu,ap,bt]UD[Amup[bt][t,x,y,z],Ϛ[ap]],{ap,0,3},{bt,0,3}] + I ZGen[LocalFieldNumber,9][ii,jj]CommuteGammastdowndown[mu,nu][[aa,bb]]Sum[UD[Am[ap][t,x,y,z],Ϛ[ap]],{ap,0,3}] + I ZGen[LocalFieldNumber,10][ii,jj]Sum[CommuteGammastdowndown[ap,mu][[aa,bb]]UD[Am[nu][t,x,y,z],Ϛ[ap]]-CommuteGammastdowndown[ap,nu][[aa,bb]]UD[Am[mu][t,x,y,z],Ϛ[ap]],{ap,0,3}]

Do[ZTable[LocalFieldNumber][mu,nu] = Table[Z[LocalFieldNumber][mu,nu][ii,jj][aa,bb],{ii,1,2},{aa,1,4},{jj,1,2},{bb,1,4}],{mu,0,3},{nu,0,3}];

Λ[tt1,tt2][nu_][ii_,jj_][aa_,bb_][t,x,y,z] := 2 I ZGen[LocalFieldNumber,11][ii,jj]Cmetric[[aa,bb]]Am[nu][t,x,y,z] +I ZGen[LocalFieldNumber,12][ii,jj]Sum[ CommuteGammastdowndown[nu,ap][[aa,bb]]Amup[ap][t,x,y,z],{ap,0,3}]  + I ZGen[LocalFieldNumber,13][ii,jj] γstdowndown[nu][[aa,bb]]A[t,x,y,z] + ZGen[LocalFieldNumber,14][ii,jj] γ5γstdowndown[nu][[aa,bb]] B[t,x,y,z]

Do[ΛTable[tt1,tt2][nu][t,x,y,z] = Table[Λ[tt1,tt2][nu][ii,jj][aa,bb][t,x,y,z],{ii,1,2},{aa,1,4},{jj,1,2},{bb,1,4}],{nu,0,3}];

AlgebraDDMinusClosure[tt1,tt2][LocalFieldNumber]=Table[(Collect[(AlgebraDD[tt1,tt2][Bmn[mu,nu][t,x,y,z]] - (ZTable[LocalFieldNumber][mu,nu]-(D[ΛTable[tt1,tt2][nu][t,x,y,z],Ϛ[mu]]-D[ΛTable[tt1,tt2][mu][t,x,y,z],Ϛ[nu]])))/.LagrangianParameters/.VtoPauli,FieldListWithDerivatives,Simplify]),{mu,0,3},{nu,0,3}];

AlgebraDDMinusClosure[tt1,tt2][14][[2,3,1,4,2]]

AlgebraDDEqs[tt1,tt2][LocalFieldNumber] = DeleteCases[Table[(Coefficient[AlgebraDDMinusClosure[tt1,tt2][LocalFieldNumber][[mu,nu,ii,aa,jj,bb]],FieldListWithDerivatives[[FieldListIndex]]])==0,{mu,1,4},{nu,1,4},{ii,1,2},{aa,1,4},{jj,1,2},{bb,1,4},{FieldListIndex,1,Length[FieldListWithDerivatives]}]//Simplify//Flatten,True]//DeleteDuplicates;

Length[AlgebraDDEqs[tt1,tt2][LocalFieldNumber]]

ZSolutions[LocalFieldNumber] = Solve[AlgebraDDEqs[tt1,tt2][LocalFieldNumber],CentralChargeList[LocalFieldNumber]]//Flatten

{(Subscript[D, a]^i),(Subscript[(OverTilde[D]), b]^j)}(Subscript[B, μν])=  2 i ((Z[lfn,1])^ij)(Subscript[([(Subscript[γ, μ]),(Subscript[γ, ν])](γ^α)), ab])(∂_α)A+2 i ((Z[lfn,2])^ij)(Subscript[((γ^α)[(Subscript[γ, μ]),(Subscript[γ, ν])]), ab])(∂_α)A 
+ 2 ((Z[lfn,3])^ij)(Subscript[((γ^5)[(Subscript[γ, μ]),(Subscript[γ, ν])](γ^α)), ab])(∂_α)B+2 ((Z[lfn,4])^ij)(Subscript[((γ^5)(γ^α)[(Subscript[γ, μ]),(Subscript[γ, ν])]), ab])(∂_α)B+ 2 i ((Z[lfn,5])^ij)(Subscript[([(Subscript[γ, μ]),(Subscript[γ, ν])]), ab])F+ 2 ((Z[lfn,6])^ij)(Subscript[((γ^5)[(Subscript[γ, μ]),(Subscript[γ, ν])]), ab])G+ 2 ((Z[lfn,7])^ij)(Subscript[((γ^5)[(Subscript[γ, μ]),(Subscript[γ, ν])]), ab])d+((Z[lfn,8])^ij)(Subscript[((γ^5)), ab])(Subscript[ϵ, μναβ])(∂^α)(A^β)+i ((Z[lfn,9])^ij)(Subscript[([(Subscript[γ, μ]),(Subscript[γ, ν])]), ab])(∂^α)(Subscript[A, α])+i ((Z[lfn,10])^ij)(Subscript[([(Subscript[γ, α]),(Subscript[γ, [μ])]), |ab|])(∂^α)(Subscript[A, ν]])-(∂_([μ))(Subscript[(OverTilde[Λ]), ν]ab]^ij)
FieldNumber = 14
(Subscript[(OverTilde[Λ]), νab]^ij)= 2i ((Z[lfn,11])^ij)(Subscript[C, ab])(Subscript[A, ν])+ i (Subscript[((Z[lfn,12])^ij)[(Subscript[γ, ν]),(Subscript[γ, α])], ab])(A^α) 
+i ((Z[lfn,13])^ij)(Subscript[((Subscript[γ, ν])), ab])A + ((Z[lfn,14])^ij)(Subscript[((γ^5)(Subscript[γ, ν])), ab])B 
The Z[11] through Z[14] are actually gauge charges

Apparently z[14,1,mu] are arbitrary, set to zero

BChoice = {z[14,1,mu_]-> 0, z[14,3,mu_]->0};

DeleteCases[Table[Z[LocalFieldNumber,nn]==PrintSigmaProduct[Table[ZGen[LocalFieldNumber,nn][ii,jj],{ii,1,2},{jj,1,2}]/.ZSolutions[LocalFieldNumber]/.ThisOneLooksGood/.BChoice],{nn,1,NumZCharges}],Z[_,_]==0]

Clear[LocalFieldNumber,NumZCharges]

Double check that no solution has vanishing central charges, there is no solution even without invoking BosonSolutions for the tilde-tilde cases.

tt1
tt2

ScalarNumbersList[tt1,tt2] = {1,2,3,4,5,8,9,10,11,12};

ScalarCentralChargeList = Table[CentralChargeList[ScalarNumbersList[tt1,tt2][[Index]]],{Index,1,Length[ScalarNumbersList[tt1,tt2]]}]//Flatten;

VectorCentralChargeList = Table[CentralChargeList[7][[Index]],{Index,1,32}]

TensorCentralChargeList = Table[CentralChargeList[14][[Index]],{Index,1,40}]

CompleteCentralChargeList = Join[ScalarCentralChargeList,VectorCentralChargeList,TensorCentralChargeList];

Dimensions[CompleteCentralChargeList]

VanishingScalarCentralChargesEqsLHS = Table[CentralChargeList[ScalarNumbersList[tt1,tt2][[Index]]]/.ZSolutions[ScalarNumbersList[tt1,tt2][[Index]]],{Index,1,Length[ScalarNumbersList[tt1,tt2]]}]//Flatten;

Dimensions[VanishingScalarCentralChargesEqsLHS]

VanishingVectorCentralChargesEqsLHS = VectorCentralChargeList/.ZSolutions[7];

VanishingTensorCentralChargesEqsLHS = TensorCentralChargeList/.ZSolutions[14];

Dimensions[VanishingVectorCentralChargesEqsLHS]

VanishingCentralChargesEqsLHS = Join[VanishingScalarCentralChargesEqsLHS,VanishingVectorCentralChargesEqsLHS,VanishingTensorCentralChargesEqsLHS];

Dimensions[VanishingCentralChargesEqsLHS]

VanishingCentralChargesEqs = DeleteCases[Table[VanishingCentralChargesEqsLHS[[Index]] ==0,{Index,1,Length[VanishingCentralChargesEqsLHS]}],True];

Dimensions[VanishingCentralChargesEqs]

VanishingCentralChargesEqs

cvList

Solve[VanishingCentralChargesEqs,cvList]

{(Subscript[D, a]^i),(Subscript[(OverTilde[D]), b]^j)}(Subscript[Ψ, c]^k)= 2 i ((Z[lfn,1])^ijkl)(Subscript[((γ^μ)), ab])(∂_μ)(Subscript[(OverTilde[Ψ]), c]^l)+2 i ((Z[lfn,2])^ijkl)(Subscript[([(γ^μ),(γ^ν)]), ab])((Subscript[((Subscript[γ, ν])), c])^d)(∂_μ)(Subscript[(OverTilde[Ψ]), d]^l)
+2 i ((Z[lfn,3])^ijkl)(Subscript[((Subscript[γ, ν])), ab])((Subscript[([(γ^ν),(γ^μ)]), c])^d)(∂_μ)(Subscript[(OverTilde[Ψ]), d]^l)+2 i ((Z[lfn,4])^ijkl)(Subscript[((γ^5)[(γ^μ),(γ^ν)]), ab])((Subscript[((γ^5)(Subscript[γ, ν])), c])^d)(∂_μ)(Subscript[(OverTilde[Ψ]), d]^l)
+2 i ((Z[lfn,5])^ijkl)(Subscript[((γ^5)(γ^μ)), ab])((Subscript[((γ^5)), c])^d)(∂_μ)(Subscript[(OverTilde[Ψ]), d]^l)+2 i ((Z[lfn,6])^ijkl)(Subscript[((γ^5)(Subscript[γ, ν])), ab])((Subscript[((γ^5)[(γ^ν),(γ^μ)]), c])^d)(∂_μ)(Subscript[(OverTilde[Ψ]), d]^l)
+2 i ((Z[lfn,7])^ijkl)(Subscript[((γ^5)), ab])((Subscript[((γ^5)(γ^μ)), c])^d)(∂_μ)(Subscript[(OverTilde[Ψ]), d]^l)+2 i ((Z[lfn,8])^ijkl)((Subscript[(Subscript[C, ab])((γ^μ)), c])^d)(∂_μ)(Subscript[(OverTilde[Ψ]), d]^l)
FieldNumber = 6

LocalFieldNumber = 6;
NumZCharges = 8;
CentralChargeList[LocalFieldNumber] = Table[z[LocalFieldNumber,FieldNumber][ii,jj,kk,ll],{FieldNumber,1,NumZCharges},{ii,1,2},{jj,1,2},{kk,1,2},{ll,1,2}]//Flatten

Length[CentralChargeList[LocalFieldNumber]]==128

Z[LocalFieldNumber][ii_,jj_,kk_][aa_,bb_,cc_]:=2 I Sum[z[LocalFieldNumber,1][ii,jj,kk,ll]γdown[mu][[aa,bb]]D[Ψt[ll][cc][t,x,y,z],Ϛ[mu]],{ll,1,2},{mu,0,3}]+2I Sum[z[LocalFieldNumber,2][ii,jj,kk,ll]CommuteGammadown[mu,nu][[aa,bb]]γstdown[nu][[cc,dd]]D[Ψt[ll][dd][t,x,y,z],Ϛ[mu]],{ll,1,2},{dd,1,4},{mu,0,3},{nu,0,3}]+2I Sum[z[LocalFieldNumber,3][ii,jj,kk,ll]γstdowndown[nu][[aa,bb]]CommuteGamma[nu,mu][[cc,dd]]D[Ψt[ll][dd][t,x,y,z],Ϛ[mu]],{ll,1,2},{dd,1,4},{mu,0,3},{nu,0,3}]+2I Sum[z[LocalFieldNumber,4][ii,jj,kk,ll](γ5.CommuteGammadown[mu,nu])[[aa,bb]]γ5γstdown[nu][[cc,dd]]D[Ψt[ll][dd][t,x,y,z],Ϛ[mu]],{ll,1,2},{dd,1,4},{mu,0,3},{nu,0,3}]+2 I Sum[z[LocalFieldNumber,5][ii,jj,kk,ll]γ5γdown[mu][[aa,bb]]γ5[[cc,dd]]D[Ψt[ll][dd][t,x,y,z],Ϛ[mu]],{ll,1,2},{mu,0,3},{dd,1,4}]+2I Sum[z[LocalFieldNumber,6][ii,jj,kk,ll]γ5γstdowndown[nu][[aa,bb]](γ5.CommuteGamma[nu,mu])[[cc,dd]]D[Ψt[ll][dd][t,x,y,z],Ϛ[mu]],{ll,1,2},{dd,1,4},{mu,0,3},{nu,0,3}]+2 I Sum[z[LocalFieldNumber,7][ii,jj,kk,ll]γ5down[[aa,bb]]γ5γ[mu][[cc,dd]]D[Ψt[ll][dd][t,x,y,z],Ϛ[mu]],{ll,1,2},{mu,0,3},{dd,1,4}]+2 I Sum[z[LocalFieldNumber,8][ii,jj,kk,ll]Cmetric[[aa,bb]]γ[mu][[cc,dd]]D[Ψt[ll][dd][t,x,y,z],Ϛ[mu]],{ll,1,2},{mu,0,3},{dd,1,4}]

Do[ZTable[LocalFieldNumber][kk,cc] = Table[Z[LocalFieldNumber][ii,jj,kk][aa,bb,cc],{ii,1,2},{aa,1,4},{jj,1,2},{bb,1,4}],{kk,1,2},{cc,1,4}];

AlgebraDDMinusClosure[tt1,tt2][LocalFieldNumber]=Table[(Collect[(AlgebraDD[tt1,tt2][Ψ[kk][cc][t,x,y,z]] - ZTable[LocalFieldNumber][kk,cc])/.LagrangianParameters/.VtoPauli,FieldListWithDerivatives,Simplify]),{kk,1,2},{cc,1,4}];

AlgebraDDEqs[tt1,tt2][LocalFieldNumber] = DeleteCases[Table[(Coefficient[AlgebraDDMinusClosure[tt1,tt2][LocalFieldNumber][[kk,cc,ii,aa,jj,bb]],FieldListWithDerivatives[[FieldListIndex]]])==0,{kk,1,2},{cc,1,4},{ii,1,2},{aa,1,4},{jj,1,2},{bb,1,4},{FieldListIndex,1,Length[FieldListWithDerivatives]}]//Simplify//Flatten,True]//DeleteDuplicates;

ZSolutions[LocalFieldNumber] = Solve[AlgebraDDEqs[tt1,tt2][LocalFieldNumber],CentralChargeList[LocalFieldNumber]]//Flatten;

Length[ZSolutions[LocalFieldNumber]]

NonZeroz[LocalFieldNumber] =DeleteCases[Table[z[LocalFieldNumber,nn][ii,jj,kk,ll]==(z[LocalFieldNumber,nn][ii,jj,kk,ll]/.ZSolutions[LocalFieldNumber]/.ThisOneLooksGood),{nn,1,NumZCharges},{ii,1,2},{jj,1,2},{kk,1,2},{ll,1,2}]//Flatten,z[_,_][_,_,_,_]==0]

ZGen[LocalFieldNumber,1][1,1]

zGenList  = Table[z[LocalFieldNumber,nn,sgNum],{nn,1,6},{sgNum,0,3}]//Flatten

(* The below Ansatz is commented out, only have 9-12 which we rename below 1-4 *)

(*zAnsatz[lfn_,nn_][ii_,jj_,kk_,ll_]:=cz[lfn,nn,1]KroneckerDelta[ii,jj]I sigma[2][[kk,ll]]+cz[lfn,nn,2]KroneckerDelta[ii,kk]I sigma[2][[jj,ll]] +cz[lfn,nn,3]KroneckerDelta[ii,ll]I sigma[2][[jj,kk]]+cz[lfn,nn,4]KroneckerDelta[jj,kk]I sigma[2][[ii,ll]]+cz[lfn,nn,5]KroneckerDelta[jj,ll]I sigma[2][[ii,kk]]+cz[lfn,nn,6]KroneckerDelta[kk,ll]I sigma[2][[ii,jj]]+cz[lfn,nn,7]sigma[3][[ii,jj]]sigma[1][[kk,ll]]+cz[lfn,nn,8]sigma[3][[ii,kk]]sigma[1][[jj,ll]]+cz[lfn,nn,9]sigma[3][[ii,ll]]sigma[1][[jj,kk]]+cz[lfn,nn,10]sigma[3][[jj,kk]]sigma[1][[ii,ll]]+cz[lfn,nn,11]sigma[3][[jj,ll]]sigma[1][[ii,kk]]+cz[lfn,nn,12]sigma[3][[kk,ll]]sigma[1][[ii,jj]]*)

zAnsatz[lfn_,nn_][ii_,jj_,kk_,ll_]:=cz[lfn,nn,1]sigma[3][[ii,ll]]sigma[1][[jj,kk]]+cz[lfn,nn,2]sigma[3][[jj,kk]]sigma[1][[ii,ll]]+cz[lfn,nn,3]sigma[3][[jj,ll]]sigma[1][[ii,kk]]+cz[lfn,nn,4]sigma[3][[kk,ll]]sigma[1][[ii,jj]]

czList[lfn_,nn_]:= Table[cz[lfn,nn,Index],{Index,1,4}]

(*zAnsatzEqs[LocalFieldNumber,1]=DeleteCases[Table[(zAnsatz[LocalFieldNumber,1][ii,jj,kk,ll])==(z[LocalFieldNumber,1][ii,jj,kk,ll]/.ZSolutions[LocalFieldNumber]/.ThisOneLooksGood),{ii,1,2},{jj,1,2},{kk,1,2},{ll,1,2}]//Flatten,True]*)

(*Solve[zAnsatzEqs[LocalFieldNumber,1],czList[LocalFieldNumber,1]]/.cz[6,1,4]->0/.cz[6,1,5]->0/.cz[6,1,6]->0/.cz[6,1,7]->0/.cz[6,1,8]->0/.cz[6,1,1]->0/.cz[6,1,2]->0/.cz[6,1,3]->0*)

Do[zAnsatzEqs[LocalFieldNumber,ZChargeNum]=DeleteCases[Table[(zAnsatz[LocalFieldNumber,ZChargeNum][ii,jj,kk,ll])==(z[LocalFieldNumber,ZChargeNum][ii,jj,kk,ll]/.ZSolutions[LocalFieldNumber]/.ThisOneLooksGood),{ii,1,2},{jj,1,2},{kk,1,2},{ll,1,2}]//Flatten,True],{ZChargeNum,1,NumZCharges}]

zSolution[LocalFieldNumber]=Table[Solve[zAnsatzEqs[LocalFieldNumber,ZChargeNum],czList[LocalFieldNumber,ZChargeNum]],{ZChargeNum,1,NumZCharges}]//Flatten

{(Subscript[D, a]^i),(Subscript[(OverTilde[D]), b]^j)}(Subscript[Ψ, c]^k)= 2 i ((Z[lfn,1])^ijkl)(Subscript[((γ^μ)), ab])(∂_μ)(Subscript[(OverTilde[Ψ]), c]^l)+2 i ((Z[lfn,3])^ijkl)(Subscript[([(γ^μ),(γ^ν)]), ab])((Subscript[((Subscript[γ, ν])), c])^d)(∂_μ)(Subscript[(OverTilde[Ψ]), d]^l)
+2 i ((Z[lfn,5])^ijkl)(Subscript[((Subscript[γ, ν])), ab])((Subscript[([(γ^ν),(γ^μ)]), c])^d)(∂_μ)(Subscript[(OverTilde[Ψ]), d]^l)+2 i ((Z[lfn,7])^ijkl)(Subscript[((γ^5)[(γ^μ),(γ^ν)]), ab])((Subscript[((γ^5)(Subscript[γ, ν])), c])^d)(∂_μ)(Subscript[(OverTilde[Ψ]), d]^l)
+2 i ((Z[lfn,9])^ijkl)(Subscript[((γ^5)(γ^μ)), ab])((Subscript[((γ^5)), c])^d)(∂_μ)(Subscript[(OverTilde[Ψ]), d]^l)+2 i ((Z[lfn,11])^ijkl)(Subscript[((γ^5)(Subscript[γ, ν])), ab])((Subscript[((γ^5)[(γ^ν),(γ^μ)]), c])^d)(∂_μ)(Subscript[(OverTilde[Ψ]), d]^l)
+2 i ((Z[lfn,13])^ijkl)(Subscript[((γ^5)), ab])((Subscript[((γ^5)(γ^μ)), c])^d)(∂_μ)(Subscript[(OverTilde[Ψ]), d]^l)+2 i ((Z[lfn,15])^ijkl)((Subscript[(Subscript[C, ab])((γ^μ)), c])^d)(∂_μ)(Subscript[(OverTilde[Ψ]), d]^l)
FieldNumber = 6

LocalFieldNumber =6;
NumZCharges = 8;
ZPrintout[LocalFieldNumber]= Table[(Subscript[Z, nn]^ijkl)== (cz[LocalFieldNumber,nn,1]((((σ^3)))^il)((((σ^1)))^jk) + cz[LocalFieldNumber,nn,2]((((σ^3)))^jk)((((σ^1)))^il) + cz[LocalFieldNumber,nn,3]((((σ^3)))^jl)((((σ^1)))^ik)+cz[LocalFieldNumber,nn,4]((((σ^3)))^kl)((((σ^1)))^ij)  )/.zSolution[LocalFieldNumber],{nn,1,NumZCharges}]
ZPrintoutTeXForm[LocalFieldNumber ] = TeXForm[%]

ZPrintout[LocalFieldNumber]= Table[(Subscript[Z, nn]^ijkl)== (cz[LocalFieldNumber,nn,1]((((σ^3)))^il)((((σ^1)))^jk) + cz[LocalFieldNumber,nn,2]((((σ^3)))^jk)((((σ^1)))^il) + cz[LocalFieldNumber,nn,3]((((σ^3)))^jl)((((σ^1)))^ik)+cz[LocalFieldNumber,nn,4]((((σ^3)))^kl)((((σ^1)))^ij)  )/.zSolution[LocalFieldNumber],{nn,1,NumZCharges}]
ZPrintoutTeXForm[LocalFieldNumber ] = TeXForm[%]

Clear[LocalFieldNumber,NumZCharges]

{(Subscript[D, a]^i),(Subscript[(OverTilde[D]), b]^j)}(Subscript[(OverTilde[Ψ]), c]^k)= 2 i ((Z[lfn,1])^ijkl)(Subscript[((γ^μ)), ab])(∂_μ)(Subscript[Ψ, c]^l)+2 i ((Z[lfn,2])^ijkl)(Subscript[([(γ^μ),(γ^ν)]), ab])((Subscript[((Subscript[γ, ν])), c])^d)(∂_μ)(Subscript[Ψ, d]^l)
+2 i ((Z[lfn,3])^ijkl)(Subscript[((Subscript[γ, ν])), ab])((Subscript[([(γ^ν),(γ^μ)]), c])^d)(∂_μ)(Subscript[Ψ, d]^l)+2 i ((Z[lfn,4])^ijkl)(Subscript[((γ^5)[(γ^μ),(γ^ν)]), ab])((Subscript[((γ^5)(Subscript[γ, ν])), c])^d)(∂_μ)(Subscript[Ψ, d]^l)
+2 i ((Z[lfn,5])^ijkl)(Subscript[((γ^5)(γ^μ)), ab])((Subscript[((γ^5)), c])^d)(∂_μ)(Subscript[Ψ, d]^l)+2 i ((Z[lfn,6])^ijkl)(Subscript[((γ^5)(Subscript[γ, ν])), ab])((Subscript[((γ^5)[(γ^ν),(γ^μ)]), c])^d)(∂_μ)(Subscript[Ψ, d]^l)
+2 i ((Z[lfn,7])^ijkl)(Subscript[((γ^5)), ab])((Subscript[((γ^5)(γ^μ)), c])^d)(∂_μ)(Subscript[Ψ, d]^l)+2 i ((Z[lfn,8])^ijkl)((Subscript[(Subscript[C, ab])((γ^μ)), c])^d)(∂_μ)(Subscript[Ψ, d]^l)
FieldNumber = 13

LocalFieldNumber = 13;
NumZCharges = 8;
CentralChargeList[LocalFieldNumber] = Table[z[LocalFieldNumber,FieldNumber][ii,jj,kk,ll],{FieldNumber,1,NumZCharges},{ii,1,2},{jj,1,2},{kk,1,2},{ll,1,2}]//Flatten;

Z[LocalFieldNumber][ii_,jj_,kk_][aa_,bb_,cc_]:=2 I Sum[z[LocalFieldNumber,1][ii,jj,kk,ll]γdown[mu][[aa,bb]]D[Ψ[ll][cc][t,x,y,z],Ϛ[mu]],{ll,1,2},{mu,0,3}]+2I Sum[z[LocalFieldNumber,2][ii,jj,kk,ll]CommuteGammadown[mu,nu][[aa,bb]]γstdown[nu][[cc,dd]]D[Ψ[ll][dd][t,x,y,z],Ϛ[mu]],{ll,1,2},{dd,1,4},{mu,0,3},{nu,0,3}]+2I Sum[z[LocalFieldNumber,3][ii,jj,kk,ll]γstdowndown[nu][[aa,bb]]CommuteGamma[nu,mu][[cc,dd]]D[Ψ[ll][dd][t,x,y,z],Ϛ[mu]],{ll,1,2},{dd,1,4},{mu,0,3},{nu,0,3}]+2I Sum[z[LocalFieldNumber,4][ii,jj,kk,ll](γ5.CommuteGammadown[mu,nu])[[aa,bb]]γ5γstdown[nu][[cc,dd]]D[Ψ[ll][dd][t,x,y,z],Ϛ[mu]],{ll,1,2},{dd,1,4},{mu,0,3},{nu,0,3}]+2 I Sum[z[LocalFieldNumber,5][ii,jj,kk,ll]γ5γdown[mu][[aa,bb]]γ5[[cc,dd]]D[Ψ[ll][dd][t,x,y,z],Ϛ[mu]],{ll,1,2},{mu,0,3},{dd,1,4}]+2I Sum[z[LocalFieldNumber,6][ii,jj,kk,ll]γ5γstdowndown[nu][[aa,bb]](γ5.CommuteGamma[nu,mu])[[cc,dd]]D[Ψ[ll][dd][t,x,y,z],Ϛ[mu]],{ll,1,2},{dd,1,4},{mu,0,3},{nu,0,3}]+2 I Sum[z[LocalFieldNumber,7][ii,jj,kk,ll]γ5down[[aa,bb]]γ5γ[mu][[cc,dd]]D[Ψ[ll][dd][t,x,y,z],Ϛ[mu]],{ll,1,2},{mu,0,3},{dd,1,4}]+2 I Sum[z[LocalFieldNumber,8][ii,jj,kk,ll]Cmetric[[aa,bb]]γ[mu][[cc,dd]]D[Ψ[ll][dd][t,x,y,z],Ϛ[mu]],{ll,1,2},{mu,0,3},{dd,1,4}]

Do[ZTable[LocalFieldNumber][kk,cc] = Table[Z[LocalFieldNumber][ii,jj,kk][aa,bb,cc],{ii,1,2},{aa,1,4},{jj,1,2},{bb,1,4}],{kk,1,2},{cc,1,4}];

AlgebraDDMinusClosure[tt1,tt2][LocalFieldNumber]=Table[(Collect[(AlgebraDD[tt1,tt2][Ψt[kk][cc][t,x,y,z]] - ZTable[LocalFieldNumber][kk,cc])/.LagrangianParameters/.VtoPauli,FieldListWithDerivatives,Simplify]),{kk,1,2},{cc,1,4}];

AlgebraDDEqs[tt1,tt2][LocalFieldNumber] = DeleteCases[Table[(Coefficient[AlgebraDDMinusClosure[tt1,tt2][LocalFieldNumber][[kk,cc,ii,aa,jj,bb]],FieldListWithDerivatives[[FieldListIndex]]])==0,{kk,1,2},{cc,1,4},{ii,1,2},{aa,1,4},{jj,1,2},{bb,1,4},{FieldListIndex,1,Length[FieldListWithDerivatives]}]//Simplify//Flatten,True]//DeleteDuplicates;

ZSolutions[LocalFieldNumber] = Solve[AlgebraDDEqs[tt1,tt2][LocalFieldNumber],CentralChargeList[LocalFieldNumber]]//Flatten;

Length[ZSolutions[LocalFieldNumber]]

NonZeroz[LocalFieldNumber] =DeleteCases[Table[z[LocalFieldNumber,nn][ii,jj,kk,ll]==(z[LocalFieldNumber,nn][ii,jj,kk,ll]/.ZSolutions[LocalFieldNumber]/.ThisOneLooksGood),{nn,1,NumZCharges},{ii,1,2},{jj,1,2},{kk,1,2},{ll,1,2}]//Flatten,z[_,_][_,_,_,_]==0]

zAnsatz[lfn_,nn_][ii_,jj_,kk_,ll_]:=cz[lfn,nn,1]sigma[3][[ii,ll]]sigma[1][[jj,kk]]+cz[lfn,nn,2]sigma[3][[jj,kk]]sigma[1][[ii,ll]]+cz[lfn,nn,3]sigma[3][[jj,ll]]sigma[1][[ii,kk]]+cz[lfn,nn,4]sigma[3][[kk,ll]]sigma[1][[ii,jj]]

czList[lfn_,nn_]:= Table[cz[lfn,nn,Index],{Index,1,4}]

Do[zAnsatzEqs[LocalFieldNumber,ZChargeNum]=DeleteCases[Table[(zAnsatz[LocalFieldNumber,ZChargeNum][ii,jj,kk,ll])==(z[LocalFieldNumber,ZChargeNum][ii,jj,kk,ll]/.ZSolutions[LocalFieldNumber]/.ThisOneLooksGood),{ii,1,2},{jj,1,2},{kk,1,2},{ll,1,2}]//Flatten,True],{ZChargeNum,1,NumZCharges}]

zSolution[LocalFieldNumber]=Table[Solve[zAnsatzEqs[LocalFieldNumber,ZChargeNum],czList[LocalFieldNumber,ZChargeNum]],{ZChargeNum,1,NumZCharges}]//Flatten

{(Subscript[D, a]^i),(Subscript[(OverTilde[D]), b]^j)}(Subscript[(OverTilde[Ψ]), c]^k)= 2 i ((Z[lfn,1])^ijkl)(Subscript[((γ^μ)), ab])(∂_μ)(Subscript[Ψ, c]^l)+2 i ((Z[lfn,3])^ijkl)(Subscript[([(γ^μ),(γ^ν)]), ab])((Subscript[((Subscript[γ, ν])), c])^d)(∂_μ)(Subscript[Ψ, d]^l)
+2 i ((Z[lfn,5])^ijkl)(Subscript[((Subscript[γ, ν])), ab])((Subscript[([(γ^ν),(γ^μ)]), c])^d)(∂_μ)(Subscript[Ψ, d]^l)+2 i ((Z[lfn,7])^ijkl)(Subscript[((γ^5)[(γ^μ),(γ^ν)]), ab])((Subscript[((γ^5)(Subscript[γ, ν])), c])^d)(∂_μ)(Subscript[Ψ, d]^l)
+2 i ((Z[lfn,9])^ijkl)(Subscript[((γ^5)(γ^μ)), ab])((Subscript[((γ^5)), c])^d)(∂_μ)(Subscript[Ψ, d]^l)+2 i ((Z[lfn,11])^ijkl)(Subscript[((γ^5)(Subscript[γ, ν])), ab])((Subscript[((γ^5)[(γ^ν),(γ^μ)]), c])^d)(∂_μ)(Subscript[Ψ, d]^l)
+2 i ((Z[lfn,13])^ijkl)(Subscript[((γ^5)), ab])((Subscript[((γ^5)(γ^μ)), c])^d)(∂_μ)(Subscript[Ψ, d]^l)+2 i ((Z[lfn,15])^ijkl)((Subscript[(Subscript[C, ab])((γ^μ)), c])^d)(∂_μ)(Subscript[Ψ, d]^l)
FieldNumber = 13

ZPrintout[LocalFieldNumber]= Table[(Subscript[(OverTilde[Z]), nn]^ijkl)== (cz[LocalFieldNumber,nn,1]((((σ^3)))^il)((((σ^1)))^jk) + cz[LocalFieldNumber,nn,2]((((σ^3)))^jk)((((σ^1)))^il) + cz[LocalFieldNumber,nn,3]((((σ^3)))^jl)((((σ^1)))^ik)+cz[LocalFieldNumber,nn,4]((((σ^3)))^kl)((((σ^1)))^ij)  )/.zSolution[LocalFieldNumber],{nn,1,NumZCharges}]
ZPrintoutTeXForm[LocalFieldNumber ] = TeXForm[%]

Clear[LocalFieldNumber,NumZCharges]