Dualities of corner configurations and supersymmetric indices

We compute supersymmetric indices which count local operators at certain half-BPS interfaces and quarter-BPS junctions of interfaces in four-dimensional N$$ \mathcal{N} $$ = 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.