Gravity as an ensemble and the moment problem

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Gravity as an ensemble and the moment problem. / Janssen, Oliver; Mirbabayi, Mehrdad; Zograf, Peter.

In: Journal of High Energy Physics, Vol. 2021, No. 6, 184, 06.2021.

Research output: Contribution to journal › Article › peer-review

Author

Janssen, Oliver ; Mirbabayi, Mehrdad ; Zograf, Peter. / Gravity as an ensemble and the moment problem. In: Journal of High Energy Physics. 2021 ; Vol. 2021, No. 6.

BibTeX

@article{9abfc536854748dbb4ac8d67013aacf0,

title = "Gravity as an ensemble and the moment problem",

abstract = "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.",

keywords = "2D Gravity, Models of Quantum Gravity",

author = "Oliver Janssen and Mehrdad Mirbabayi and Peter Zograf",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s).",

year = "2021",

month = jun,

doi = "10.1007/JHEP06(2021)184",

language = "English",

volume = "2021",

journal = "Journal of High Energy Physics",

issn = "1126-6708",

publisher = "Springer Nature",

number = "6",

}

RIS

TY - JOUR

T1 - Gravity as an ensemble and the moment problem

AU - Janssen, Oliver

AU - Mirbabayi, Mehrdad

AU - Zograf, Peter

PY - 2021/6

Y1 - 2021/6

N2 - 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.

AB - 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.

KW - 2D Gravity

KW - Models of Quantum Gravity

UR - http://www.scopus.com/inward/record.url?scp=85109111728&partnerID=8YFLogxK

U2 - 10.1007/JHEP06(2021)184

DO - 10.1007/JHEP06(2021)184

M3 - Article

AN - SCOPUS:85109111728

VL - 2021

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 6

M1 - 184

ER -

ID: 98426342