On the Superconformal Index of Argyres-Douglas Theories

TL;DR

This paper proposes a closed-form expression for the superconformal index of certain Argyres-Douglas theories, connecting 4D SCFTs with 2D q-deformed Yang-Mills theory and class S data, and validates it through multiple consistency checks.

Contribution

It introduces a novel conjecture for the superconformal index of (A_1,A_{2n-3}) and (A_1,D_{2n}) Argyres-Douglas theories using relations to 2D q-deformed Yang-Mills and class S constructions.

Findings

Derived explicit formulas for the indices of the theories.

Validated the formulas through S-duality and RG flow consistency.

Reproduced known Higgs branch relations and Cardy-like limits.

Abstract

We conjecture a closed-form expression for the Schur limit of the superconformal index of two infinite series of Argyres-Douglas (AD) superconformal field theories (SCFTs): the (A_1,A_{2n-3}) and the (A_1,D_{2n}) theories. While these SCFTs can be realized at special points on the Coulomb branch of certain N=2 gauge theories, their superconformal R symmetries are emergent, and hence their indices cannot be evaluated by localization. Instead, we construct the (A_1, A_{2n-3}) and (A_1, D_{2n}) indices by using a relation to two-dimensional q-deformed Yang-Mills theory and data from the class S construction. Our results generalize the indices derived from the torus partition functions of the two-dimensional chiral algebras associated with the (A_1, A_3) and (A_1, D_4) SCFTs. As checks of our conjectures, we study the consistency of our results with an S-duality recently discussed by us in collaboration with Giacomelli and Papageorgakis, we reproduce known Higgs branch relations, we check consistency with a series of renormalization group flows, and we verify that the small S^1 limits of our indices reproduce expected Cardy-like behavior. We will discuss the S^1 reduction of our indices in a separate paper.