Stephen Ebert, Eliot Hijano, Per Kraus, Ruben Monten, Richard M. Myers
SciPost Phys. 13, 038 (2022) ·
published 29 August 2022
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· pdf
Pure three-dimensional gravity is a renormalizable theory with two free
parameters labelled by $G$ and $\Lambda$. As a consequence, correlation
functions of the boundary stress tensor in AdS$_3$ are uniquely fixed in terms
of one dimensionless parameter, which is the central charge of the Virasoro
algebra. The same argument implies that AdS$_3$ gravity at a finite radial
cutoff is a renormalizable theory, but now with one additional parameter
corresponding to the cutoff location. This theory is conjecturally dual to a
$T\overline{T}$-deformed CFT, assuming that such theories actually exist. To
elucidate this, we study the quantum theory of boundary gravitons living on a
cutoff planar boundary and the associated correlation functions of the boundary
stress tensor. We compute stress tensor correlation functions to two-loop order
($G$ being the loop counting parameter), extending existing tree level results.
This is made feasible by the fact that the boundary graviton action 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 single undetermined renormalization parameter.
