Super-Rényi Entropy & Wilson Loops for N=4 SYM and their Gravity Duals

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We compute the supersymmetric Rényi entropies across a spherical entanglement surface in N=4 SU(N) SYM theory using localization on the four-dimensional ellipsoid. We extract the leading result at large N and λ, and match its universal part to a gravity calculation involving a hyperbolically sliced supersymmetric black hole solution of N=4+ SU(2) X U(1) gauged supergravity in five dimensions. We repeat the analysis in the presence of a Wilson loop insertion and find again a perfect match with the dual string theory. Understanding the Wilson loop operator requires knowledge of the full ten-dimensional IIB supergravity solution which we elaborate upon.