Argyres-Douglas Theories, S-duality and AGT Correspondence

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.

46 pages, 3 figures

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• Infinitely many 4d $\mathcal{N}=2$ SCFTs with $a=c$ and beyond
• On the Nekrasov Partition Function of Gauged Argyres-Douglas Theories
• Partition functions of non-Lagrangian theories from the holomorphic anomaly
• Connection formulae in the Collision Limit I: Case Studies in Lifshitz Geometry