Real-time gravitational replicas: formalism and a variational principle

• Published in: The journal of high energy physics Vol. 2021; no. 5; pp. 1 - 40
• Main Authors: Colin-Ellerin, Sean, Dong, Xi, Marolf, Donald, Rangamani, Mukund, Wang, Zhencheng
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2021; Springer Nature B.V; Springer Nature; SpringerOpen
• Subjects: AdS-CFT Correspondence; Approximation; Boundary conditions; Classical and Quantum Gravitation; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Elementary Particles; Euclidean space; Field theory; Gauge-gravity correspondence; Gravity; High energy physics; Integrals; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Real time; Regular Article - Theoretical Physics; Relativity Theory; Saddle points; Saddles; String Theory; Wormholes; AdS-CFT Correspondence; Gauge-gravity correspondence
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP05(2021)117

A bstract This work is the first step in a two-part investigation of real-time replica wormholes. Here we study the associated real-time gravitational path integral and construct the variational principle that will define its saddle-points. We also describe the general structure of the resulting real-time replica wormhole saddles, setting the stage for construction of explicit examples. These saddles necessarily involve complex metrics, and thus are accessed by deforming the original real contour of integration. However, the construction of these saddles need not rely on analytic continuation, and our formulation can be used even in the presence of non-analytic boundary-sources. Furthermore, at least for replica- and CPT-symmetric saddles we show that the metrics may be taken to be real in regions spacelike separated from a so-called ‘splitting surface’. This feature is an important hallmark of unitarity in a field theory dual.