Gauge Theories on ALE Space and Super Liouville Correlation Functions

TL;DR

This paper establishes a novel correspondence between N=2 quiver gauge theories on ALE spaces and super Liouville conformal field theory, deriving formulas and matching partition functions with conformal blocks and three-point functions.

Contribution

It introduces a blow-up formula for Nekrasov partition functions and connects gauge theory instanton sums with super Liouville correlators, extending the gauge/CFT correspondence.

Findings

Derived a blow-up formula for Nekrasov partition functions.

Showed the N=2* instanton partition function relates to super Virasoro blocks.

Matched perturbative gauge contributions with super Liouville three-point functions.

Abstract

We present a relation between N=2 quiver gauge theories on the ALE space O_{P^1}(-2) and correlators of N=1 super Liouville conformal field theory, providing checks in the case of punctured spheres and tori. We derive a blow-up formula for the full Nekrasov partition function and show that, up to a U(1) factor, the N=2^* instanton partition function is given by the product of the character of \hat{SU}(2)_2 times the super Virasoro conformal block on the torus with one puncture. Moreover, we match the perturbative gauge theory contribution with super Liouville three-point functions.