Field Theory of Interacting Boundary Gravitons

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.

arXiv comment71 pages, 1 figure, typos corrected and clarifications added in response to the referees' questions

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Cited by in corpus (17)

• $T\bar{T}$ in JT Gravity and BF Gauge Theory
• Root-$T\overline{T}$ Deformed Boundary Conditions in Holography
• Stress Tensor Flows, Birefringence in Non-Linear Electrodynamics, and Supersymmetry
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• $T\overline{T}$-Like Flows and $3d$ Nonlinear Supersymmetry
• ModMax Oscillators and Root-$T\overline{T}$-Like Flows in Supersymmetric Quantum Mechanics
• Flows in the Space of Interacting Chiral Boson Theories
• $T\bar{T}+{\Lambda }_2$ from a 2d gravity path integral
• One-loop partition functions in $T\overline{T}$-deformed AdS${}_3$
• Systematics of Boundary Actions in Gauge Theory and Gravity
• Systematic approach to correlators in $T\bar{T}$ deformed CFTs
• Gravitational wavefunctions in JT supergravity
• On the Charge Algebra of Causal Diamonds in Three Dimensional Gravity
• Root-$T\overline{T}$ deformed CFT partition functions at large central charge
• Probing holography in $p$-adic CFT
• Locality and Conserved Charges in $T\overline{T}$-Deformed CFTs
• The chiral SYK model in three-dimensional holography