Replica wormholes from Liouville theory

Abstract

The replica wormholes are a key to the existence of the islands that play a central role in a recent proposal for the resolution of the black hole information paradox. In this paper, we study the replica wormholes in the JT gravity, a model of two-dimensional quantum gravity coupled to a non-dynamical dilaton, by making use of the 2d conformal field theory (CFT) description, namely, the Liouville theory coupled to the (2, p) minimal matter in the p → ∞ limit. In the Liouville CFT description, the replica wormholes are created by the twist operators and the gravitational part of the bulk entanglement entropy can be reproduced from the twist operator correlators. We propose the precise dictionary and show how this correspondence works in detail.

Entanglement between two evaporating black holes

“…The island contribution originates from so-called replica wormholes connecting different replicas in computing the von Neumann entropy of the Hawking radiation by using the replica trick in the semi-classical description of gravity [8,9]. See also e.g., for discussions on the island formula, and e.g., [65][66][67][68][69][70][71] on replica wormholes. C m E Q k T F B U K q l q 2 3 z 3 0 s P B y S a S 3 J 9 G x M k p x w v h g J B i o 9 7 3 c O R a Z p 7 d u X 5 k x M V A W l 1 3 T Q 3 L x F j 3 F d G i c E + l R 0 A J d i 3 + 1 a / M w A A V O 3 e 0 m 5 r h 4 q Z Z + F r o r m X m 3 W w u V k F R x n 4 S 6 u n z e X Y z J j Z a s E u 9 I m r y s K i P 3 K K 3 U P L 6 R 5 1 Q B V q 5 e p m f A q e 5 q b 6 2 f v F f w d O T s E Z j j g T G P g E B h y G C s f n 8 F N a J t t O y j F Y L v J s k X v Z 3 v T y 0 M e I c Z X W y l 5 U 1 u N b E t z C Y L T C U a G D h w V 4 j T m Y l N i 3 5 I S g 6 y K q V 0 A t u / D C B p J a 7 p 1 A O Q F v f n t f 3 y O 6 a 6 9 o l S r F 0 c V N S I O 0 x D k B v s o e U y b B U I S M y Y k F J I 7 0 q B 8 7 I 7 B q k g D z N P N + W 3 / s q L n e K b X 4 p / 1 e 9 7 m l f j v t T q X 5 i 8 F n 5 O R p T l 7 P 6 X b s J K d d T + q m S Q t p R w 8 j H j E f D The Penrose diagram of an AdS black hole coupled to the non-gravitating external bath.…”

Solvable models of quantum black holes: a review on Jackiw–Teitelboim gravity

“…An important recent result is that these models are not independent, but JT gravity can be embedded in Liouville gravity. This was first noticed for the spectrum in Saad et al (2019), and subsequently developed in detail in Mertens and Turiaci (2021), Mertens (2021), Turiaci et al (2021), Fan and Mertens (2022a), Suzuki and Takayanagi (2021), Hirano andKuroki (2022), Artemev (2022).…”

“…( 2019 ), and subsequently developed in detail in Mertens and Turiaci ( 2021 ), Mertens ( 2021 ), Turiaci et al. ( 2021 ), Fan and Mertens ( 2022a ), Suzuki and Takayanagi ( 2021 ), Hirano and Kuroki ( 2022 ), Artemev ( 2022 ).…”

Page curve from dynamical branes in JT gravity

“…Another way to obtain JT gravity is to take the p → ∞ limit of the (2, p) minimal string[21,36].Entanglement entropy in this context was studied recently in[37] 5. This shift of couplings was first recognized in the theory of soliton equations[38] and appears in various contexts of matrix models and related subjects.…”