# Dualities of Corner Configurations and Supersymmetric Indices

## TL;DR

This paper calculates supersymmetric indices for specific BPS defects in 4D N=4 Super Yang-Mills theory to test string theory-inspired S-duality conjectures on these configurations.

## Contribution

It introduces a method to compute indices for BPS interfaces and junctions, providing new tests for S-duality actions on these defects.

## Key findings

- Supersymmetric indices successfully match S-duality predictions.
- New insights into the structure of BPS defects in N=4 Super Yang-Mills.
- Validation of string theory conjectures through index calculations.

## Abstract

We compute supersymmetric indices which count local operators at certain half-BPS interfaces and quarter-BPS junctions of interfaces in four-dimensional $\mathcal{N}=4$ Super Yang-Mills theory. We use the indices as very stringent tests of a variety of string theory-inspired conjectures about the action of S-duality on such defects.