, Volume 101, Issue 1, pp 103-124
Date: 21 Mar 2012

Gauge Theories on ALE Space and Super Liouville Correlation Functions

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Abstract

We present a relation between \({\mathcal{N}=2}\) quiver gauge theories on the ALE space \({\mathcal{O}_{\mathbb{P}^1}(-2)}\) and correlators of \({\mathcal{N}=1}\) 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 \({\mathcal{N}=2^*}\) instanton partition function is given by the product of the character of \({\widehat{SU}(2)_2}\) 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.