Semiclassical 3D gravity as an average of large-c CFTs

• Published in: The journal of high energy physics Vol. 2022; no. 12; pp. 69 - 82
• Main Authors: Chandra, Jeevan, Collier, Scott, Hartman, Thomas, Maloney, Alexander
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 13.12.2022; Springer Nature B.V; SpringerOpen
• Subjects: AdS-CFT Correspondence; Black Holes; Black Holes in String Theory; Classical and Quantum Gravitation; Couplings; Elementary Particles; Energy spectra; Field Theories in Lower Dimensions; Gravitation theory; Gravity; High energy physics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Topology; Wormholes; Black Holes in String Theory; AdS-CFT Correspondence; Field Theories in Lower Dimensions; Black Holes
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP12(2022)069

A bstract A two-dimensional CFT dual to a semiclassical theory of gravity in three dimensions must have a large central charge c and a sparse low energy spectrum. This constrains the OPE coefficients and density of states of the CFT via the conformal bootstrap. We define an ensemble of CFT data by averaging over OPE coefficients subject to these bootstrap constraints, and show that calculations in this ensemble reproduce semiclassical 3D gravity. We analyze a wide variety of gravitational solutions, both in pure Einstein gravity and gravity coupled to massive point particles, including Euclidean wormholes with multiple boundaries and higher topology spacetimes with a single boundary. In all cases we find that the on-shell action of gravity agrees with the ensemble-averaged CFT at large c . The one-loop corrections also match in the cases where they have been computed. We also show that the bulk effective theory has random couplings induced by wormholes, providing a controlled, semiclassical realization of the mechanism of Coleman, Giddings, and Strominger.