For a vector field X and a spinor ψ, we can define the modified Seiberg-Witten equations:
DXψ=(D+iX)ψ=0
id(X∗)+=−(1/4)w(ψ)/|ψ|2
with D the Dirac operator, X∗ is the dual 1-form of X; + is the self-dual part and w is the 2-form bound to the spinor ψ.
The gauge group acts: f.(X,ψ)=(X−(df)∗,ifψ)
Have we compact moduli spaces?