A bstract Recent developments involving JT gravity in two dimensions indicate that under some conditions, a gravitational path integral is dual to an average over an ensemble of boundary theories, rather than to a specific boundary theory. For an example in one dimension more, one would like to compare a random ensemble of twodimensional CFT’s to Einstein gravity in three dimensions. But this is difficult. For a simpler problem, here we average over Narain’s family of twodimensional CFT’s obtained by toroidal compactification. These theories are believed to be the most general ones with their central charges and abelian current algebra symmetries, so averaging over them means picking a random CFT with those properties. The average can be computed using the SiegelWeil formula of number theory and has some properties suggestive of a bulk dual theory that would be an exotic theory of gravity in three dimensions. The bulk dual theory would be more like U(1) 2 D ChernSimons theory than like Einstein gravity.
Matrix models and deformations of JT gravity
Recently, it has been found that JackiwTeitelboim (JT) gravity, which is a twodimensional theory with bulk action − 1 / 2 ∫ d 2 x g ϕ ( 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 ∫ d 2 x g ( ϕ R + 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.
 Award ID(s):
 1911298
 Publication Date:
 NSFPAR ID:
 10233811
 Journal Name:
 Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
 Volume:
 476
 Issue:
 2244
 Page Range or eLocationID:
 20200582
 ISSN:
 13645021
 Sponsoring Org:
 National Science Foundation
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