Entanglement Renyi Entropies in Conformal Field Theories and Holography

TL;DR

This paper investigates entanglement Renyi entropies in conformal field theories with holographic duals, computes the divergent part in N=4 super Yang-Mills, and proposes a holographic formula involving minimal hypersurfaces.

Contribution

It introduces a holographic formula for Renyi entropies based on minimal hypersurfaces, extending the understanding of entanglement in conformal theories with gravity duals.

Findings

Divergent part of Renyi entropy computed in N=4 super Yang-Mills

Holographic formula reproduces leading order Renyi entropy

Holographic Renyi entropy involves invariant functionals on minimal hypersurfaces

Abstract

An entanglement Renyi entropy for a spatial partition of a system is studied in conformal theories which admit a dual description in terms of an anti-de Sitter gravity. The divergent part of the Renyi entropy is computed in 4D conformal N=4 super Yang-Mills theory at a weak coupling. This result is used to suggest a holographic formula which reproduces the Renyi entropy at least in the leading approximation. The holographic Renyi entropy is an invariant functional set on a codimension 2 minimal hypersurface in the bulk geometry. The bulk space does not depend on order $n$ of the Renyi entropy. The holographic Renyi entropy is a sum of local and non-local functionals multiplied by polynomials of $1/n$.