%AEbert, Stephen%AHijano, Eliot%AKraus, Per%AMonten, Ruben%AMyers, Richard%BJournal Name: SciPost Physics; Journal Volume: 13; Journal Issue: 2
%D2022%ISci Post
%JJournal Name: SciPost Physics; Journal Volume: 13; Journal Issue: 2
%K
%MOSTI ID: 10469670
%PMedium: X
%TField Theory of Interacting Boundary Gravitons
%XPure three-dimensional gravity is a renormalizable theory with twofree parameters labelled byG$G$and\Lambda$\Lambda $.As a consequence, correlation functions of the boundary stress tensor inAdS_3${}_{3}$are uniquely fixed in terms of one dimensionless parameter, which is thecentral charge of the Virasoro algebra. The same argument implies thatAdS_3${}_{3}$gravity at a finite radial cutoff is a renormalizable theory, but nowwith one additional parameter corresponding to the cutoff location. Thistheory is conjecturally dual to aT\overline{T}$T\overline{T}$-deformedCFT, assuming that such theories actually exist. To elucidate this, westudy the quantum theory of boundary gravitons living on a cutoff planarboundary and the associated correlation functions of the boundary stresstensor. We compute stress tensor correlation functions to two-loop order(G$G$being the loop counting parameter), extending existing tree levelresults. This is made feasible by the fact that the boundary gravitonaction simplifies greatly upon making a judicious field redefinition,turning into the Nambu-Goto action. After imposing Lorentz invariance,the correlators at this order are found to be unambiguous up to a singleundetermined renormalization parameter.

%0Journal Article