Gravity duals of boundary cones

TL;DR

This paper explores gravity duals of boundary cones related to Renyi entropies, constructing new solutions for complex shapes and analyzing their properties and implications for holographic entropy calculations.

Contribution

It introduces new bulk solutions for conical singularities of arbitrary shapes in holography, extending previous known solutions and analyzing their properties and implications.

Findings

Reproduces known logarithmic divergence structures of Renyi entropies.

Constructs new perturbative solutions for non-spherical conical singularities.

Supports a non-minimal resolution to the splitting problem in higher-derivative theories.

Abstract

The replica trick defines Renyi entropies as partition functions on conically singular geometries. We discuss their gravity duals: regular bulk solutions to the Einstein equations inducing conically singular metrics at the boundary. When the conical singularity is supported on a flat or spherical surface, these solutions are rewritings of the hyperbolic black hole. For more general shapes, these solutions are new. We construct them perturbatively in a double expansion in the distance and strength of the conical singularity, and extract the vacuum polarisation due to the cone. Recent results about the structure of logarithmic divergences of Renyi entropies are reproduced ---in particular, $f_b\neq f_c$. We discuss in detail the dynamical resolution of the singularity in the bulk. This resolution is in agreement with a previous proposal, and indicates a non-minimal settling to the `splitting problem': an apparent ambiguity in the holographic entropy formula of certain theories with higher derivatives.