The gravity dual of supersymmetric Renyi entropy

Supersymmetric Renyi entropies are defined for three-dimensional N = 2 superconformal field theories on a branched covering of a three-sphere by using the localized partition functions. Under a conformal transformation, the branched covering is mapped to S-1 x H-2, whose gravity dual is the charged topological AdS(4) black hole. The black hole can be embedded into four-dimensional N = 2 gauged supergravity where the mass and charge are related so that it preserves half of the supersymmetries. We compute the supersymmetric Renyi entropies with and without a certain type of Wilson loop operators in the gravity theory. We find they agree with those of the dual field theories in the large-N limit.