$n$-th parafermion $\mathcal{W}_N$ characters from $U(N)$ instanton counting on ${\mathbb {C}}^2/{\mathbb {Z}}_n$

Abstract

We propose, following the AGT correspondence, how the $\mathcal{W}^{\, para}_{N, n}$ ($n$-th parafermion $\mathcal{W}_N$) minimal model characters are obtained from the $U(N)$ instanton counting on ${\mathbb {C}}^2/{\mathbb {Z}}_n$ with $\Omega$-deformation by imposing specific conditions which remove the minimal model null states.