Establishing strongly-coupled 3D AdS quantum gravity with Ising dual using all-genus partition functions
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Received: February 24, 2020 Accepted: September 15, 2020 Published: October 20, 2020
Establishing strongly-coupled 3D AdS quantum gravity with Ising dual using all-genus partition functions
a
Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106-4030, U.S.A. b Department of Physics, University of California, Santa Barbara, CA 93106-9530, U.S.A. c Department of Physics and Astronomy, University of Utah, Salt Lake City, UT 84112-0830, U.S.A. d Center for Theoretical Physics and Department of Physics, University of California, Berkeley, CA 94720-7300, U.S.A. e Microsoft Station Q, Santa Barbara, CA 93106-6105, U.S.A. f Department of Mathematics, University of California, Santa Barbara, CA 93106-3080, U.S.A.
E-mail: [email protected], zhuxi [email protected], [email protected], [email protected] Abstract: We study 3D pure Einstein quantum gravity with negative cosmological constant, in the regime where the AdS radius l is of the order of the Planck scale. Specifically, when the Brown-Henneaux central charge c = 3l/2GN (GN is the 3D Newton constant) equals c = 1/2, we establish duality between 3D gravity and 2D Ising conformal field theory by matching gravity and conformal field theory partition functions for AdS spacetimes with general asymptotic boundaries. This duality was suggested by a genus-one calculation of Castro et al. [Phys. Rev. D 85 (2012) 024032]. Extension beyond genus-one requires new mathematical results based on 3D Topological Quantum Field Theory; these turn out to uniquely select the c = 1/2 theory among all those with c < 1, extending the previous results of Castro et al.. Previous work suggests the reduction of the calculation of the gravity partition function to a problem of summation over the orbits of the mapping class group action on a “vacuum seed”. But whether or not the summation is well-defined for the general case was unknown before this work. Amongst all theories with Brown-Henneaux central charge c < 1, the sum is finite and unique only when c = 1/2, corresponding to a dual Ising conformal field theory on the asymptotic boundary. Keywords: AdS-CFT Correspondence, Topological Field Theories, Models of Quantum Gravity, Conformal Field Theory ArXiv ePrint: 1907.06656
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)129
JHEP10(2020)129
Chao-Ming Jian,a Andreas W. W. Ludwig,b Zhu-Xi Luo,a,c Hao-Yu Suna,d and Zhenghan Wange,f
Contents 1 Introduction and summary of results
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2 Gravitational partition function with torus asymptotic boundary 2.1 Vacuum seed 2.2 Modular sum and duality to the Ising CFT
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4 Gravitational partition functions with boundaries of arbitrary genus 4.1 Vacuum seed 4.2 Finiteness of the modular sum 4.3 Irreducibility of the MCG representation and the modular sum 4.4 Duality to 2D Ising CFT 4.5 Difficulty in extending beyond the 2D Ising CFT
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A Genus one modular sum revisited
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B Generators for Sp(4, Z) and the a
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