I asked a question here where a moduli space of flat connection is related to the $n$-dimensional complex projective space: $$\Bbb E/S_n \cong \Bbb P^{n-1}. $$ This is related to a 4d SU(N) Yang-Mills theory compactified on a 2d 2-torus.
question 1. Do we have some examples where the moduli space of flat connection are nontrivial Calabi-Yau manifolds?
question 2. I also encounter the word moduli space of instantons.
What are the definitions of "moduli space of flat connections" v.s. moduli space of instantons"? What are the differences and their relations?