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

TL;DR

This paper calculates supersymmetric Rénnyi entropies and Wilson loop observables in N=4 SYM theory using localization, and matches these results with gravity duals involving supersymmetric black holes and string theory, confirming the AdS/CFT correspondence.

Contribution

It provides a detailed computation of Rénnyi entropies and Wilson loops in N=4 SYM and establishes precise matches with their gravity duals, including the full ten-dimensional supergravity solutions.

Findings

Universal part of Rénnyi entropy matches gravity calculations.

Wilson loop results agree with dual string theory predictions.

Explicit gravity dual solutions are constructed and analyzed.

Abstract

We compute the supersymmetric R\'enyi 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 \lambda, 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.