# Field Theory of Interacting Boundary Gravitons

### Submission summary

 Authors (as Contributors): Stephen Ebert · Per Kraus · Ruben Monten
Submission information
Date accepted: 2022-08-08
Date submitted: 2022-07-27 06:32
Submitted by: Monten, Ruben
Submitted to: SciPost Physics
Ontological classification
Specialties:
• High-Energy Physics - Theory
Approach: Theoretical

### Abstract

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.

Published as SciPost Phys. 13, 038 (2022)