Ramond sector of super Liouville theory from instantons on an ALE space

TL;DR

This paper establishes a correspondence between N=2 U(2) gauge theories on ALE spaces with specific holonomies and the Ramond sector of super Liouville theory, supported by matching instanton partition functions with Whittaker vector norms.

Contribution

It proposes a novel link between gauge theories on ALE spaces and super Liouville theory's Ramond sector, highlighting the role of holonomies and S-duality.

Findings

Instanton partition functions match Ramond sector inner products.

Holonomies outside SU(2) relate to Ramond boundary conditions.

S-duality exchanges different boundary sectors.

Abstract

We propose that N=2 U(2) gauge theories on the A_1 ALE space, with asymptotic holonomies not in SU(2), correspond to the Ramond sector of super Liouville theory. As evidence, we show that the instanton partition functions for the theories with and without a fundamental hypermultiplet, computed with such holonomies, coincide with the norms or the inner products of the Whittaker vectors in the Ramond sector. This correspondence suggests that S-duality of U(2) gauge theories interchanges the sectors with different boundary conditions.