Super-Rényi entropy & Wilson loops for N = 4 SYM and their gravity duals

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[superscript +] SU(2) × 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.United States. Dept. of Energy (Cooperative Research Agreement DE-FG02-05ER-41360