# N=2 S-duality Revisited

## TL;DR

This paper revisits a specific N=2 S-duality involving Argyres-Douglas theories, revealing a hidden factorization into free and interacting parts through chiral algebra bootstrap, and explores properties of the interacting component T_X.

## Contribution

It uncovers the structure of the AD SCFT T_{3,3/2} as a split into free and interacting sectors using chiral algebra bootstrap, despite the absence of a Lagrangian or SW curve.

## Key findings

- The interacting part T_X has a flavor symmetry SU(3)×SU(2)×U(1).
- The central charge of chi(T_X) matches the bc ghost central charge.
- T_X exhibits a Witten anomaly in its SU(2) symmetry.

## Abstract

Using the chiral algebra bootstrap, we revisit the simplest Argyres-Douglas (AD) generalization of Argyres-Seiberg S-duality. We argue that the exotic AD superconformal field theory (SCFT), $T_{3,{3\over2}}$, emerging in this duality splits into a free piece and an interacting piece, T_X, even though this factorization seems invisible in the Seiberg-Witten (SW) curve derived from the corresponding M5-brane construction. Without a Lagrangian, an associated topological field theory, a BPS spectrum, or even an SW curve, we nonetheless obtain exact information about T_X by bootstrapping its chiral algebra, chi(T_X), and finding the corresponding vacuum character in terms of Affine Kac-Moody characters. By a standard 4D/2D correspondence, this result gives us the Schur index for T_X and, by studying this quantity in the limit of small S^1, we make contact with a proposed S^1 reduction. Along the way, we discuss various properties of T_X: as an N=1 theory, it has flavor symmetry SU(3)XSU(2)XU(1), the central charge of chi(T_X) matches the central charge of the bc ghosts in bosonic string theory, and its global SU(2) symmetry has a Witten anomaly. This anomaly does not prevent us from building conformal manifolds out of arbitrary numbers of T_X theories (giving us a surprisingly close AD relative of Gaiotto's T_N theories), but it does lead to some open questions in the context of the chiral algebra / 4D N=2 SCFT correspondence.