The Gravity Dual of Renyi Entropy

TL;DR

This paper extends the holographic principle to Renyi entropies, showing they follow an area law similar to entanglement entropy and are computed via dual cosmic branes, enabling new insights into quantum entanglement in gravity.

Contribution

It introduces a geometric prescription for all Renyi entropies in holography using cosmic branes, generalizing the minimal surface approach for entanglement entropy.

Findings

Renyi entropies satisfy an area law in holographic theories.

All Renyi entropies are given by areas of dual cosmic branes.

First holographic calculation of mutual Renyi information between two disks.

Abstract

A remarkable yet mysterious property of black holes is that their entropy is proportional to the horizon area. This area law inspired the holographic principle, which was later realized concretely in gauge/gravity duality. In this context, entanglement entropy is given by the area of a minimal surface in a dual spacetime. However, discussions of area laws have been constrained to entanglement entropy, whereas a full understanding of a quantum state requires Renyi entropies. Here we show that all Renyi entropies satisfy a similar area law in holographic theories and are given by the areas of dual cosmic branes. This geometric prescription is a one-parameter generalization of the minimal surface prescription for entanglement entropy. Applying this we provide the first holographic calculation of mutual Renyi information between two disks of arbitrary dimension. Our results provide a framework for efficiently studying Renyi entropies and understanding entanglement structures in strongly coupled systems and quantum gravity.