Argyres-Douglas Theories, S-duality and AGT Correspondence

Abstract

We propose a Nekrasov-type formula for the instanton partition functions of fourdimensional N = 2 U (2) gauge theories coupled to (A 1 , D 2n ) Argyres-Douglas theories. This is carried out by extending the generalized AGT correspondence to the case of U (2) gauge group, which requires us to define irregular states of the direct sum of Virasoro and Heisenberg algebras. Using our formula, one can evaluate the contribution of the (A 1 , D 2n ) theory at each fixed point on the U (2) instanton moduli space. As an application, we evaluate the instanton partition function of the (A 3 , A 3 ) theory to find it in a peculiar relation to that of SU (2) gauge theory with four fundamental flavors. From this relation, we read off how the S-duality group acts on the UV gauge coupling of the (A 3 , A 3 ) theory.