TY - JOUR

T1 - Matrix models and deformations of JT gravity

T2 - Matrix Models and Deformations

AU - Witten, Edward

N1 - Funding Information:
Data accessibility. This article has no additional data. Competing interests. I declare I have no competing interests. Funding. Research supported in part by NSF grant no. PHY-1911298.
Publisher Copyright:
© 2020 The Author(s).

PY - 2020/12

Y1 - 2020/12

N2 - Recently, it has been found that Jackiw-Teitelboim (JT) gravity, which is a two-dimensional theory with bulk action-1/2∫d2xgφ(R+2), is dual to a matrix model, that is, a random ensemble of quantum systems rather than a specific quantum mechanical system. In this article, we argue that a deformation of JT gravity with bulk action-1/2∫d2xg(φR+W(φ)) is likewise dual to a matrix model. With a specific procedure for defining the path integral of the theory, we determine the density of eigenvalues of the dual matrix model. There is a simple answer if W(0) = 0, and otherwise a rather complicated answer.

AB - Recently, it has been found that Jackiw-Teitelboim (JT) gravity, which is a two-dimensional theory with bulk action-1/2∫d2xgφ(R+2), is dual to a matrix model, that is, a random ensemble of quantum systems rather than a specific quantum mechanical system. In this article, we argue that a deformation of JT gravity with bulk action-1/2∫d2xg(φR+W(φ)) is likewise dual to a matrix model. With a specific procedure for defining the path integral of the theory, we determine the density of eigenvalues of the dual matrix model. There is a simple answer if W(0) = 0, and otherwise a rather complicated answer.

KW - JT gravity

KW - matrix models

KW - quantum gravity

UR - http://www.scopus.com/inward/record.url?scp=85099024464&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85099024464&partnerID=8YFLogxK

U2 - 10.1098/rspa.2020.0582

DO - 10.1098/rspa.2020.0582

M3 - Article

C2 - 33408561

AN - SCOPUS:85099024464

SN - 1364-5021

VL - 476

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

IS - 2244

M1 - 20200610

ER -