Gravity as an ensemble and the moment problem

• Published in: The journal of high energy physics 2021-06, Vol.2021 (6), p.1-19, Article 184
• Main Authors: Janssen, Oliver, Mirbabayi, Mehrdad, Zograf, Peter
• Format: Article
• Language: English
• Subjects: 2D Gravity; Classical and Quantum Gravitation; Criteria; Elementary Particles; Energy industry; Free energy; Gravitation theory; Gravity; High energy physics; Models of Quantum Gravity; Partitions (mathematics); Perturbation theory; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Supergravity; Two dimensional models; Uniqueness
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP06(2021)184

A bstract If a bulk gravitational path integral can be identified with an average of partition functions over an ensemble of boundary quantum theories, then a corresponding moment problem can be solved. We review existence and uniqueness criteria for the Stieltjes moment problem, which include an infinite set of positivity conditions. The existence criteria are useful to rule out an ensemble interpretation of a theory of gravity, or to indicate incompleteness of the gravitational data. We illustrate this in a particular class of 2D gravities including variants of the CGHS model and JT supergravity. The uniqueness criterion is relevant for an unambiguous determination of quantities such as log Z β ¯ or the quenched free energy. We prove in JT gravity that perturbation theory, both in the coupling which suppresses higher-genus surfaces and in the temperature, fails when the number of boundaries is taken to infinity. Since this asymptotic data is necessary for the uniqueness problem, the question cannot be settled without a nonperturbative completion of the theory.