$n$-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 ${\mathcal{W}}_{N,n}^{para}$ ($n$-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.

25 pages, 2 figures; v2: minor changes, references added; I would like to dedicate this paper to the memory of Professor Omar Foda

References in corpus (2)

• Conformal blocks of W_N Minimal Models and AGT correspondence
• N=1 superconformal blocks with Ramond fields from AGT correspondence