Argyres-Douglas Theories, S-duality and AGT Correspondence

TL;DR

This paper extends the AGT correspondence to U(2) gauge theories coupled with Argyres-Douglas theories, providing a Nekrasov-type formula for instanton partition functions and exploring S-duality actions.

Contribution

It introduces a generalized AGT framework for U(2) theories with irregular states, enabling explicit computation of instanton contributions for Argyres-Douglas theories.

Findings

Derived a Nekrasov-type formula for (A_1,D_{2n}) theories.

Evaluated the (A_3,A_3) instanton partition function.

Revealed the S-duality action on the UV gauge coupling.

Abstract

We propose a Nekrasov-type formula for the instanton partition functions of four-dimensional 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.