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We compute the supersymmetric R\'enyi entropies across a sphericalentanglement surface in N=4 SU(N) SYM theory using localization on thefour-dimensional ellipsoid. We extract the leading result at large N and\lambda, and match its universal part to a gravity calculation involving ahyperbolically sliced supersymmetric black hole solution of N=4+ SU(2) X U(1)gauged supergravity in five dimensions. We repeat the analysis in the presenceof a Wilson loop insertion and find again a perfect match with the dual stringtheory. Understanding the Wilson loop operator requires knowledge of the fullten-dimensional IIB supergravity solution which we elaborate upon.

Super-R\'enyi Entropy & Wilson Loops for N=4 SYM and their Gravity Duals