Field Theory of Interacting Boundary Gravitons

Ebert, Stephen; Hijano, Eliot; Kraus, Per; Monten, Ruben; Myers, Richard M.

doi:10.21468/SciPostPhys.13.2.038

SciPost Physics

Field Theory of Interacting Boundary Gravitons

Stephen Ebert, Eliot Hijano, Per Kraus, Ruben Monten, Richard M. Myers

SciPost Phys. 13, 038 (2022) · published 29 August 2022

doi: 10.21468/SciPostPhys.13.2.038
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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.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.13.2.038
TI  - Field Theory of Interacting Boundary Gravitons
PY  - 2022/08/29
UR  - https://scipost.org/SciPostPhys.13.2.038
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 13
IS  - 2
SP  - 038
A1  - Ebert, Stephen
AU  - Hijano, Eliot
AU  - Kraus, Per
AU  - Monten, Ruben
AU  - Myers, Richard M.
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.13.2.038,
	title={{Field Theory of Interacting Boundary Gravitons}},
	author={Stephen Ebert and Eliot Hijano and Per Kraus and Ruben Monten and Richard M. Myers},
	journal={SciPost Phys.},
	volume={13},
	pages={038},
	year={2022},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.13.2.038},
	url={https://scipost.org/10.21468/SciPostPhys.13.2.038},
}

Cited by 11

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¹ Stephen Ebert,
² Eliot Hijano,
¹ Per Kraus,
¹ Ruben Monten,
¹ Richard M. Myers

Funders for the research work leading to this publication