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 δ ≤ 0.19. This means in particular that unlike the second Rnyi entropy, the third one is no longer universal.
Belin, A., Keller, C., Zadeh, I. (2017). Genus two partition functions and Rényi entropies of large c conformal field theories. JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL, 50(43) [10.1088/1751-8121/aa8a11].
Genus two partition functions and Rényi entropies of large c conformal field theories
Belin A;
2017
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 δ ≤ 0.19. This means in particular that unlike the second Rnyi entropy, the third one is no longer universal.
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