N=2 S-duality Revisited

Understand

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.