# Non-analyticity of holographic R\'enyi entropy in Lovelock gravity

## TL;DR

This paper investigates how third order Lovelock gravity affects holographic Renyi entropies, revealing phase transitions and non-analytic behavior in the dual conformal field theories.

## Contribution

It provides the first analysis of holographic Renyi entropies in third order Lovelock gravity, identifying phase transitions and boundary causality constraints.

## Key findings

- Lovelock black holes with hyperbolic horizons are unstable.
- Phase transitions occur at low temperatures for smaller mass black holes.
- Renyi entropy exhibits a kink at a critical index n.

## Abstract

We compute holographic R\'enyi entropies for spherical entangling surfaces on the boundary while considering third order Lovelock gravity with negative cosmological constant in the bulk. Our study shows that third order Lovelock black holes with hyperbolic event horizon are unstable, and at low temperatures those with smaller mass are favoured, giving rise to first order phase transitions in the bulk. We determine regions in the Lovelock parameter space in arbitrary dimensions, where bulk phase transitions happen and where boundary causality constraints are met. We show that each of these points corresponds to a dual boundary conformal field theory whose R\'enyi entropy exhibits a kink at a certain critical index $n$.