Genus Two Partition Functions and Renyi Entropies of Large c CFTs

Understand

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.