Interface line operators in $\mathcal{N}=4$ SYM theories and supersymmetric indices

TL;DR

This paper investigates BPS interface line operators in $ ext{N}=4$ super Yang-Mills theories, demonstrating S-duality through matching line defect indices and deriving explicit closed-form formulas involving $q$-binomials and Schur functions.

Contribution

It provides the first detailed analysis of interface line operators in $ ext{N}=4$ SYM, including explicit formulas for their indices and evidence for S-duality of such configurations.

Findings

Line defect half-indices match under S-duality.

Explicit closed-form formulas involving $q$-binomials and Schur functions.

Strong evidence supporting S-duality of interface line operators.

Abstract

We study configurations of two $\mathcal{N}=4$ super Yang-Mills theories of unitary gauge groups connected by the BPS interfaces involving line operators. We find strong evidence of S-duality of the configurations as precise matching of the line defect half-indices which enumerate the BPS local operators at the junctions of the interfaces and line operators. The interface line defect half-indices are expressible as intriguing closed-form formulae involving the $q$-binomial coefficients and the principal specializations of the Schur functions.