Field Theory of Interacting Boundary Gravitons

TL;DR

This paper investigates the quantum properties of boundary gravitons in three-dimensional AdS gravity with a finite cutoff, revealing how their correlation functions relate to a conjectured dual $T\overline{T}$-deformed CFT and extending previous tree-level results to two loops.

Contribution

It provides a two-loop computation of boundary stress tensor correlators in cutoff AdS$_3$ gravity, demonstrating the simplification of the boundary graviton action and clarifying the quantum structure of the theory.

Findings

Correlation functions are fixed up to one renormalization parameter.

Boundary graviton action simplifies to the Nambu-Goto form.

Results support the duality with $T\overline{T}$-deformed CFTs.

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.