Let (M,g) be a spin manifold, the Dirac equations are acting on (X,Y,ψ), two vector fields and a spinor:
X.∇Yψ=(a/b)∇YX.ψ
D(X.ψ)=((a/b)+1)dX.ψ
Y.∇Xψ=(a/c)∇XY.ψ
D(Y.ψ)=((a/c)+1)dY.ψ
with D the Dirac operator.
The gauge group is G=C∞(M,R∗+) and acts:
f.(ψ,X,Y)=(faψ,fbX,fcY)
The moduli space is M(M)=S(X,Y,ψ)/G.
Is the moduli space finite dimensional and can we define invariants?