Comments on the double cone wormhole

• Published in: The journal of high energy physics Vol. 2024; no. 4; pp. 124 - 48
• Main Authors: Chen, Yiming, Ivo, Victor, Maldacena, Juan
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 23-04-2024; Springer Nature B.V; SpringerOpen
• Subjects: AdS-CFT Correspondence; Black Holes; Classical and Quantum Gravitation; Elementary Particles; Evolution; Form factors; Geometry; Holography and Hydrodynamics; Inclusions; Mathematical analysis; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Translations; Wormholes; AdS-CFT Correspondence; Holography and Hydrodynamics; Black Holes
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP04(2024)124

A
bstract
In this paper we revisit the double cone wormhole introduced by Saad, Shenker and Stanford (SSS), which was shown to reproduce the ramp in the spectral form factor. As a first approximation we can say that this solution computes Tr[
e
−iKT
], a trace of the “evolution” operator that generates Schwarzschild time translations on the two sided wormhole geometry. This point of view leads to a simple way to compute the normalization factor of the wormhole. When we have bulk matter fields, SSS suggested using a modified evolution
which involves a slightly complex geometry, so that we are really computing
. We argue that, for general black holes, the spectrum of
is given by quasinormal mode frequencies. We explain that this reproduces various features that were previously predicted from the spectral form factor on hydrodynamics grounds. We also give a general algebraic construction of the modified boost in terms of operators constructed from half sided modular inclusions. For the special case of JT gravity, we work out the backreaction of matter on the geometry of the double cone and find that it deforms the geometry in an undesirable direction. We finally give some comments on the possible physical interpretation of
.