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

Abstract

We propose that N=2U(2) gauge theories on the A1 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.