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
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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 -