Geometrizing $T\bar{T}$

Abstract

The $T\bar{T}$ deformation can be formulated as a dynamical change of coordinates. We establish and generalize this relation to curved spaces by coupling the undeformed theory to 2d gravity. For curved space the dynamical change of coordinates is supplemented by a dynamical Weyl transformation. We also sharpen the holographic correspondence to cutoff AdS${}_3$ in multiple ways. First, we show that the action of the annular region between the cutoff surface and the boundary of AdS${}_3$ is given precisely by the $T\bar{T}$ operator integrated over either the cutoff surface or the asymptotic boundary. Then we derive dynamical coordinate and Weyl transformations directly from the bulk. Finally, we reproduce the flow equation for the deformed stress tensor from the cutoff geometry.

arXiv commentv2: 28 pages, published version

References in corpus (31)

• A Stress Tensor for Anti-de Sitter Gravity
• The Holographic Weyl anomaly
• Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence
• On space of integrable quantum field theories
• $T\bar{T}$-deformed 2D Quantum Field Theories
• Asymptotic Fragility, Near $Ad{S}_2$ Holography and $T\bar{T}$
• Solving the Simplest Theory of Quantum Gravity
• Quantum effective action from the AdS/CFT correspondence
• Cutoff AdS${}_3$ versus the $T\bar{T}$ deformation
• The $T\overline{T}$ deformation of quantum field theory as random geometry
• $T\bar{T}$ Partition Function from Topological Gravity
• Holography at finite cutoff with a $T^2$ deformation
• The $\text{T}\bar{\text{T}}$ perturbation and its geometric interpretation
• $T\bar{T}$-deformations in closed form
• $T\bar{T}$ and the mirage of a bulk cutoff
• A Solvable Irrelevant Deformation of $Ad{S}_3/CF{T}_2$
• $T\bar{T}$ Deformations, Massive Gravity and Non-Critical Strings
• Wedge-Local Quantum Fields and Noncommutative Minkowski Space
• Sphere partition functions and cut-off AdS
• TsT, $T\bar{T}$ and black strings
• Expectation value of composite field $T\bar{T}$ in two-dimensional quantum field theory
• Moving the CFT into the bulk with $T\bar{T}$
• TT deformations in general dimensions
• $T\bar{T}$-Deformed Actions and (1,1) Supersymmetry
• Reconstructing AdS/CFT
• Gravitational path integral from the $T^2$ deformation
• Expectation value of $\mathrm{T}\overline{\mathrm{T}}$ operator in curved spacetimes
• Random Boundary Geometry and Gravity Dual of $T\bar{T}$ Deformation
• Cutoff $\mathrm{Ad}{\mathrm{S}}_3$ versus $\mathrm{T}\bar{\mathrm{T}}$ $\mathrm{CF}{\mathrm{T}}_2$ in the large central charge sector: correlators of energy-momentum tensor
• A $T\bar{T}$ Deformation for Curved Spacetimes from 3d Gravity
• Comments on $T\bar{T}$, $J\bar{T}$ and String Theory

Cited by in corpus (21)

• Holography from the Wheeler-DeWitt equation
• Duality-Invariant Non-linear Electrodynamics and Stress Tensor Flows
• 3D Gravity in a Box
• Field Theory of Interacting Boundary Gravitons
• Holographic Path-Integral Optimization
• Geometric formulation of generalized root-$T\bar{T}$ deformations
• Massive gravity generalization of $T\overline{T}$ deformations
• Geometrizing non-relativistic bilinear deformations
• $T\bar{T}$ Deformation of Stress-Tensor Correlators from Random Geometry
• $T\bar{T}$-flow effects on torus partition functions
• Building Tensor Networks for Holographic States
• $T\overline{T}$ deformation in SCFTs and integrable supersymmetric theories
• $T\overline{T}$-Like Flows and $3d$ Nonlinear Supersymmetry
• $T\bar{T}$ deformation on multiquantum mechanics and regenesis
• Surface charges in Chern-Simons gravity with $T\bar{T}$ deformation
• $T\overline{T}$-deformed free energy of the Airy model
• Characters of irrelevant deformations
• Locality and Conserved Charges in $T\overline{T}$-Deformed CFTs
• Metric approach to a $\mathrm{T}\bar{\mathrm{T}}-$like deformation in arbitrary dimensions
• $T\bar{T}$ deformation of Calogero-Sutherland model via dimensional reduction
• Cost of holographic path integrals