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

Dualities of Corner Configurations and Supersymmetric Indices