Root-$T\overline{T}$ Deformed Boundary Conditions in Holography

Abstract

We develop the holographic dictionary for pure ${\mathrm{AdS}}_3$ gravity where the Lagrangian of the dual $2d$ conformal field theory has been deformed by an arbitrary function of the energy-momentum tensor. In addition to the $T\overline{T}$ deformation, examples of such functions include a class of marginal stress tensor deformations which are special because they leave the generating functional of connected correlators unchanged up to a redefinition of the source and expectation value. Within this marginal class, we identify the unique deformation that commutes with the $T\overline{T}$ flow, which is the root-$T\overline{T}$ operator, and write down the modified boundary conditions corresponding to this root-$T\overline{T}$ deformation. We also identify the unique marginal stress tensor flow for the cylinder spectrum of the dual CFT which commutes with the inviscid Burgers' flow driven by $T\overline{T}$, and we propose this unique flow as a candidate root-$T\overline{T}$ deformation of the energy levels. We study BTZ black holes in ${\mathrm{AdS}}_3$ subject to root-$T\overline{T}$ deformed boundary conditions, and find that their masses flow in a way which is identical to that of our candidate root-$T\overline{T}$ energy flow equation, which offers evidence that this flow is the correct one. Finally, we also obtain the root-$T\overline{T}$ deformed boundary conditions for the gauge field in the Chern-Simons formulation of ${\mathrm{AdS}}_3$ gravity.

arXiv comment65 pages, LaTeX; v2: typos corrected and references added; v3: published version

References in corpus (54)

• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• A Stress Tensor for Anti-de Sitter Gravity
• Quasilocal Energy and Conserved Charges Derived from the Gravitational Action
• Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence
• AdS/CFT Correspondence and Symmetry Breaking
• The Kerr/CFT Correspondence
• A General Definition of "Conserved Quantities" in General Relativity and Other Theories of Gravity
• On space of integrable quantum field theories
• $T\bar{T}$-deformed 2D Quantum Field Theories
• The asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant
• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• A non-linear duality-invariant conformal extension of Maxwell's equations
• Asymptotic Fragility, Near $Ad{S}_2$ Holography and $T\bar{T}$
• Three-dimensional quantum geometry and black holes
• Quantum effective action from the AdS/CFT correspondence
• A universal result on central charges in the presence of double-trace deformations
• Cutoff AdS${}_3$ versus the $T\bar{T}$ deformation
• The $T\overline{T}$ deformation of quantum field theory as random geometry
• "Double-trace" Deformations, Boundary Conditions and Spacetime Singularities
• Multi-Trace Deformations in AdS/CFT: Exploring the Vacuum Structure of the Deformed CFT
• Holography at finite cutoff with a $T^2$ deformation
• The $\text{T}\bar{\text{T}}$ perturbation and its geometric interpretation
• Modular invariance and uniqueness of $T\bar{T}$ deformed CFT
• $T\bar{T}$ and the mirage of a bulk cutoff
• $T\bar{T}$ deformed partition functions
• Generalised Born-Infeld models, Lax operators and the $\text{T}\bar{\text{T}}$ perturbation
• Double-trace operators and one-loop vacuum energy in AdS/CFT
• On p-form gauge theories and their conformal limits
• Partition functions and double-trace deformations in AdS/CFT
• Double-Trace Deformations, Mixed Boundary Conditions and Functional Determinants in AdS/CFT
• Thermodynamics of Higher Spin Black Holes in AdS${}_3$
• Emergence of non-linear electrodynamic theories from $T\bar{T}$-like deformations
• An improved correspondence formula for AdS/CFT with multi-trace operators
• On $T\bar{T}$ deformations and supersymmetry
• The holographic interpretation of $J\bar{T}$-deformed CFTs
• Supersymmetry and $T\overline{T}$ Deformations
• Root-$T\overline{T}$ Deformations in Two-Dimensional Quantum Field Theories
• Mapping relativistic to ultra/non-relativistic conformal symmetries in 2D and finite $\sqrt{T\bar{T}}$ deformations
• Maximally symmetric nonlinear extension of electrodynamics and charged particles
• $T\bar{T}$ deformations with $\mathcal{N}=(0,2)$ supersymmetry
• $T\bar{T}$ Flows and (2,2) Supersymmetry
• Tauberian-Cardy formula with spin
• Boosting to BMS
• On the Classical Integrability of Root-$T\overline{T}$ Flows
• Nonlinear automorphism of the conformal algebra in 2D and continuous $\sqrt{T\bar{T}}$ deformations
• Non-Linear Supersymmetry and $T\bar{T}$-like Flows
• $T\bar{T}$ in JT Gravity and BF Gauge Theory
• Field Theory of Interacting Boundary Gravitons
• Marginal $T\bar{T}$-Like Deformation and ModMax Theories in Two Dimensions
• Sequential Flows by Irrelevant Operators
• $T\bar{T}$ flow as characteristic flows
• $T\overline{T}$ Deformations of Supersymmetric Quantum Mechanics
• Lax Connections in $T\bar{T}$-deformed Integrable Field Theories
• $T\bar{T}/J\bar{T}$-deformed WZW models from Chern-Simons AdS${}_3$ gravity with mixed boundary conditions

Cited by in corpus (11)

• Duality-Invariant Non-linear Electrodynamics and Stress Tensor Flows
• Interacting Chiral Form Field Theories and $T\overline{T}$-like Flows in Six and Higher Dimensions
• Geometric formulation of generalized root-$T\bar{T}$ deformations
• Stress Tensor Flows, Birefringence in Non-Linear Electrodynamics, and Supersymmetry
• ModMax Oscillators and Root-$T\overline{T}$-Like Flows in Supersymmetric Quantum Mechanics
• $T\overline{T}$-Like Flows and $3d$ Nonlinear Supersymmetry
• Flows in the Space of Interacting Chiral Boson Theories
• Irrelevant and marginal deformed BMS field theories
• Root-$T\overline{T}$ deformed CFT partition functions at large central charge
• Field-Dependent Metrics and Higher-Form Symmetries in Duality-Invariant Theories of Non-Linear Electrodynamics
• On $\sqrt{T\overline{T}}$ deformed pathways: CFT to CCFT