### 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.

Original language | English (US) |
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Article number | 435401 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 50 |

Issue number | 43 |

DOIs | |

State | Published - Sep 27 2017 |

Externally published | Yes |

### Keywords

- AdS/CFT correspondence
- conformal field theory
- genus two partition functions
- holography
- phase transition
- Renyi entanglement entropy

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modeling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)

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## Cite this

Belin, A., Keller, C. A., & Zadeh, I. G. (2017). Genus two partition functions and Rényi entropies of large c conformal field theories.

*Journal of Physics A: Mathematical and Theoretical*,*50*(43), [435401]. https://doi.org/10.1088/1751-8121/aa8a11