Bootstrapping the superconformal index with surface defects

TL;DR

This paper interprets the superconformal index's analytic properties via surface defects, enabling efficient computation of indices for generalized quiver theories with S-duality constraints.

Contribution

It introduces a method to extract residues of the superconformal index using difference operators, linking them to surface defects and enabling calculations for a broad class of theories.

Findings

Residues of the index correspond to theories with surface defects.

Difference operators of Ruijsenaars-Schneider type facilitate residue extraction.

The method applies to all generalized quiver theories of type A.

Abstract

The analytic properties of the N = 2 superconformal index are given a physical interpretation in terms of certain BPS surface defects, which arise as the IR limit of supersymmetric vortices. The residue of the index at a pole in flavor fugacity is interpreted as the index of a superconformal field theory without this flavor symmetry, but endowed with an additional surface defect. The residue can be efficiently extracted by acting on the index with a difference operator of Ruijsenaars-Schneider type. By imposing the associativity constraints of S-duality, we are then able to evaluate the index of all generalized quiver theories of type A, for generic values of the three superconformal fugacities, with or without surface defects.