Instantons on ALE spaces and Super Liouville Conformal Field Theories

TL;DR

Problem: extend AGT-type correspondences to N=1 super Liouville by considering gauge theories on ALE spaces. Approach: perform instanton counting on the minimal resolution of C^2/Z2 via algebraic geometry, derive a blow-up formula, and compare to super Liouville conformal blocks. Key results: SU(2) pure gauge theory on O_{P^1}(-2) reproduces super Liouville blocks with a precise parameter map and sector correspondence; the ALE result equals F0 + 1/2 F1, supporting a robust ALE–super Liouville link. Significance: provides a concrete bridge between 4D gauge theories on resolved singularities and 2D superconformal blocks, suggesting ADE extensions and deeper connections to Hitchin systems and integrable structures.

Abstract

We provide evidence that the conformal blocks of N=1 super Liouville conformal field theory are described in terms of the SU(2) Nekrasov partition function on the ALE space O_{P^1}(-2).