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Quantum electrodynamics (QED) is the quantum field theory believed to describe electromagnetic interaction. It is the simplest example of a quantum gauge theory, where the gauge group is abelian, U(1).
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What is $\mathcal{N}=2$ QED?
I would like to know is $\mathcal{N}=2$ QED is simply a $\mathcal{N}=2$ theory with gauge group $U(1)$ like in normal QED? If not, exactly what theory is it? Is there some reference for it?
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Counting d.o.f. and gauge fixing $A_{\mu}$ and $\psi$ in $D$-dimensions
Setup:
Let us assume we are in $D$-dimensional Minkowski space-time where $D=d+1$. Consider a free Abelian gauge theory. Then the electromagnetic field will satisfy
$$\partial_{\mu}F^{\mu \nu}=0 \ta …