Gravity as an ensemble and the moment problem
| Autor: | Mehrdad Mirbabayi, Peter Zograf, Oliver Janssen |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
High Energy Physics - Theory
Physics Nuclear and High Energy Physics Stieltjes moment problem 010308 nuclear & particles physics CGHS model FOS: Physical sciences Boundary (topology) QC770-798 Coupling (probability) 01 natural sciences Gravitation Moment problem General Relativity and Quantum Cosmology High Energy Physics - Theory (hep-th) Nuclear and particle physics. Atomic energy. Radioactivity 0103 physical sciences Models of Quantum Gravity Uniqueness Perturbation theory 010306 general physics 2D Gravity Mathematical physics |
| Zdroj: | Journal of High Energy Physics, Vol 2021, Iss 6, Pp 1-19 (2021) Journal of High Energy Physics |
| ISSN: | 1029-8479 |
| DOI: | 10.1007/jhep06(2021)184 |
| Popis: | 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 criterium is relevant for an unambiguous determination of quantities such as $\overline{\log Z(\beta)}$ 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. Comment: 11+12 pages |
| Databáze: | OpenAIRE |
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