# Mirror symmetry of 3d $\mathcal{N}=4$ gauge theories and supersymmetric indices

## TL;DR

This paper computes supersymmetric indices to verify mirror symmetry and dualities in 3d and 4d supersymmetric gauge theories, providing strong evidence for conjectured dualities and boundary conditions.

## Contribution

It introduces calculations of supersymmetric indices as a method to test and confirm mirror symmetry and dualities in 3d and 4d supersymmetric gauge theories.

## Key findings

- Matching of indices supports proposed dualities
- Evidence for mirror symmetry in 3d theories
- Validation of boundary condition dualities in 4d theories

## Abstract

We compute supersymmetric indices to test mirror symmetry of three-dimensional $\mathcal{N}=4$ gauge theories and dualities of half-BPS enriched boundary conditions and interfaces in four-dimensional $\mathcal{N}=4$ Super Yang-Mills theory. We find the matching of indices as strong evidences for various dualities of the 3d interfaces conjectured by Gaiotto and Witten under the action of S-duality in Type IIB string theory.