Infrared Computations of Defect Schur Indices

TL;DR

This paper proposes a conjecture for computing the Schur index of N=2 theories with boundary conditions or line defects using Seiberg-Witten theory, and tests it on various examples including non-Lagrangian theories.

Contribution

It introduces a new conjectural formula for defect-enriched Schur indices and demonstrates its validity across multiple non-trivial examples, including Argyres-Douglas theories.

Findings

Line defect indices can be expressed as sums of characters of 2D chiral algebras.

For Argyres-Douglas theories, the index reduces to the Verlinde algebra.

The conjecture is supported by tests on SU(2) gauge theories, both conformal and asymptotically free.

Abstract

We conjecture a formula for the Schur index of N=2 four-dimensional theories in the presence of boundary conditions and/or line defects, in terms of the low-energy effective Seiberg-Witten description of the system together with massive BPS excitations. We test our proposal in a variety of examples for SU(2) gauge theories, either conformal or asymptotically free. We use the conjecture to compute these defect-enriched Schur indices for theories which lack a Lagrangian description, such as Argyres-Douglas theories. We demonstrate in various examples that line defect indices can be expressed as sums of characters of the associated two-dimensional chiral algebra and that for Argyres-Douglas theories the line defect OPE reduces in the index to the Verlinde algebra.