Infrared computations of defect Schur indices

Abstract

We conjecture a formula for the Schur index of four-dimensional N = 2 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.

Line operators of gauge theories on non-spin manifolds

“…To find the possible spin/charge relations, first, we consider the spins of line operators resulting from the fusion of two line operators. Upon fusion, the resulting line generically sits in a reducible representation, and the fusion rules are specified by a complicated operator product expansion (OPE) whose exact form is known only in cases with sufficient supersymmetry [8,[35][36][37][38][39]. We will not need any details of the OPE -the only fact used in this article is that the fusion of line operators [ν, 6 We propose that the angular momentum stored in the electromagnetic field of the two dyons w and w ′ is…”

N = 1 $$ \mathcal{N}=1 $$ deformations and RG flows of N = 2 $$ \mathcal{N}=2 $$ SCFTs

“…Recently, the superconformal index in various limits for the Argyres-Douglas theory has been computed [49][50][51][52][53][54]. Here, we compute the full superconformal index of the ArgyresDouglas theory using the gauge theory description we obtained.…”

N $$ \mathcal{N} $$ =1 Lagrangians for generalized Argyres-Douglas theories

“…Also, it is possible to use the 3d mirror description to compute the Hall-Littlewood index [31]. There is also an interesting connection between the Schur index and the spectrum of massive BPS particles in the Coulomb branch [32][33][34][35]. The correspondence between 4d N = 2 SCFT and the 2d chiral algebra [36] gives another way of computing the Schur/Macdonald index [30,33,[37][38][39] of the Argyres-Douglas theories.…”