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

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.