TY - JOUR

T1 - Genus two partition functions and Rényi entropies of large c conformal field theories

AU - Belin, Alexandre

AU - Keller, Christoph A.

AU - Zadeh, Ida G.

N1 - Funding Information:
We would like to thank Alejandra Castro, Shouvik Datta, Jan de Boer, Ben Freivogel, Matthias Gaberdiel, Sean Hartnoll, Diego Hofman, Nabil Iqbal, Henry Maxfield for useful discussions. We thank Tom Faulkner, Tom Hartman, Matt Headrick and Alex Maloney for helpful remarks on the draft. CAK thanks the Harvard University High Energy Theory Group for hospitality. IGZ thanks Institute of Physics at the University of Amsterdam for hospitality. We thank the Galileo Galilei Institute for Theoretical Physics (GGI) for the hospitality and INFN for partial support during the completion of this work, within the program New Developments in AdS3/CFT2 Holography. In addition, IGZ thanks INFN as well as the ACRI (Associazione di Fondazioni e di Casse di Risparmio S.p.a.) for partial support through a YITP fellowship. CAK and IGZ are supported by the Swiss National Science Foundation through the NCCR SwissMAP. AB is supported by the Foundation for Fundamental Research on Matter (FOM). This work is part of the Δ-ITP consortium, a program of the NWO funded by the Dutch Ministry of Education, Culture and Science (OCW).

PY - 2017/9/27

Y1 - 2017/9/27

N2 - 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.

AB - 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.

KW - AdS/CFT correspondence

KW - Renyi entanglement entropy

KW - conformal field theory

KW - genus two partition functions

KW - holography

KW - phase transition

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U2 - 10.1088/1751-8121/aa8a11

DO - 10.1088/1751-8121/aa8a11

M3 - Article

AN - SCOPUS:85031017362

VL - 50

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 43

M1 - 435401

ER -