# Genus Two Partition Functions and Renyi Entropies of Large c CFTs

## TL;DR

This paper calculates genus two partition functions and third Renyi entropies in large c 2D CFTs, revealing a phase transition and non-universality for theories with light operators, contrasting with pure gravity results.

## Contribution

It introduces the computation of genus two partition functions for large c CFTs and identifies a phase transition affecting the universality of the third Renyi entropy.

## Key findings

- Discovery of a phase transition at light operator dimension Δ ≤ 0.19
- Third Renyi entropy is not universal in certain theories
- Comparison between free theories, orbifolds, and pure gravity results

## Abstract

We compute genus two partition functions in two dimensional conformal field theories at large central charge, focusing on surfaces that give the third Renyi entropy of two intervals. We compute this for generalized free theories and for symmetric orbifolds, and compare it to the result in pure gravity. We find a new phase transition if the theory contains a light operator of dimension $\Delta\leq0.19$. This means in particular that unlike the second Renyi entropy, the third one is no longer universal.