Stephen Ebert, Eliot Hijano, Per Kraus, Ruben Monten, Richard M. Myers
SciPost Phys. 13, 038 (2022) ·
published 29 August 2022
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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.
SciPost Phys. 11, 070 (2021) ·
published 27 September 2021
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The quantization of pure 3D gravity with Dirichlet boundary conditions on a
finite boundary is of interest both as a model of quantum gravity in which one
can compute quantities which are "more local" than S-matrices or asymptotic
boundary correlators, and for its proposed holographic duality to $T
\overline{T}$-deformed CFTs. In this work we apply covariant phase space
methods to deduce the Poisson bracket algebra of boundary observables. The
result is a one-parameter nonlinear deformation of the usual Virasoro algebra
of asymptotically AdS$_3$ gravity. This algebra should be obeyed by the stress
tensor in any $T\overline{T}$-deformed holographic CFT. We next initiate
quantization of this system within the general framework of coadjoint orbits,
obtaining - in perturbation theory - a deformed version of the
Alekseev-Shatashvili symplectic form and its associated geometric action. The
resulting energy spectrum is consistent with the expected spectrum of
$T\overline{T}$-deformed theories, although we only carry out the explicit
comparison to $\mathcal{O}(1/\sqrt{c})$ in the $1/c$ expansion.
