The $T\overline{T}$ deformation of quantum field theory as random geometry

Abstract

We revisit the results of Zamolodchikov and others on the deformation of two-dimensional quantum field theory by the determinant $\det T$ of the stress tensor, commonly referred to as $T\overline{T}$. Infinitesimally this is equivalent to a random coordinate transformation, with a local action which is, however, a total derivative and therefore gives a contribution only from boundaries or nontrivial topology. We discuss in detail the examples of a torus, a finite cylinder, a disk and a more general simply connected domain. In all cases the partition function evolves according to a linear diffusion-type equation, and the deformation may be viewed as a kind of random walk in moduli space. We also discuss possible generalizations to higher dimensions.

32 pages. Final published version! Solution for t>0 clarified

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• Exact results for curvature-driven coarsening in two dimensions
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Cited by in corpus (165)

• 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
• Entanglement entropy and $T\overline{T}$ deformation
• $T\bar{T}$ and the mirage of a bulk cutoff
• $T\bar{T}$ deformed partition functions
• A pedagogical review on solvable irrelevant deformations of 2d quantum field theory
• Entanglement Entropy in $T\overline{T}$-Deformed CFT
• $T\bar{T}$ Deformations, Massive Gravity and Non-Critical Strings
• The holographic interpretation of $J\bar{T}$-deformed CFTs
• On $T\bar{T}$ deformations and supersymmetry
• Entanglement Beyond $\mathrm{AdS}$
• Supersymmetry and $T\overline{T}$ Deformations
• $T\bar{T}$ deformed CFT as a non-critical string
• de Sitter Microstates from $T\bar{T}+{\Lambda }_2$ and the Hawking-Page Transition
• Correlation functions, entanglement and chaos in the $T\bar{T}$/$J\bar{T}$-deformed CFTs
• Root-$T\overline{T}$ Deformations in Two-Dimensional Quantum Field Theories
• TsT, $T\bar{T}$ and black strings
• Sphere partition functions and cut-off AdS
• Holographic integration of $T\bar{T}$ and $J\bar{T}$ via $O(d,d)$
• Entanglement Entropy for $TT$ deformed CFT in general dimensions
• Limits of JT gravity
• Mapping relativistic to ultra/non-relativistic conformal symmetries in 2D and finite $\sqrt{T\bar{T}}$ deformations
• Entanglement and Rényi Entropy of Multiple Intervals in $T\overline{T}$-Deformed CFT and Holography
• Correlation functions of the CFTs on torus with $T\bar{T}$ deformation
• $T\bar{T}$ deformations with $\mathcal{N}=(0,2)$ supersymmetry
• On correlation functions in $J\bar{T}$-deformed CFTs
• $T\bar{T}$-Deformed Actions and (1,1) Supersymmetry
• Modular covariance and uniqueness of $J\bar{T}$ deformed CFTs
• $T\bar{T}$ deformations and integrable spin chains
• Integrability and Renormalization under $T\bar{T}$
• $T\bar{T},J\bar{T}$, $T\bar{J}$ Partition Sums From String Theory
• Flow equations for generalised $T\bar{T}$ deformations
• Quantum chaos, scrambling and operator growth in $T\bar{T}$ deformed SYK models
• Causal Structures and Nonlocality in Double Holography
• Wilson loop in a $T\bar{T}$ like deformed ${\mathrm{CFT}}_2$
• $T\bar{T}$-like Flows in Non-linear Electrodynamic Theories and S-duality
• The correlation function of (1,1) and (2,2) supersymmetric theories with $T\bar{T}$ deformation
• $T\bar{T}$-deformation and long range spin chains
• Duality-Invariant Non-linear Electrodynamics and Stress Tensor Flows
• Gravitational path integral from the $T^2$ deformation
• KdV charges in $T\bar{T}$ theories and new models with super-Hagedorn behavior
• Expectation value of $\mathrm{T}\overline{\mathrm{T}}$ operator in curved spacetimes
• Geometrizing $T\bar{T}$
• $T\bar{T}$, the entanglement wedge cross section, and the breakdown of the split property
• On the Classical Integrability of Root-$T\overline{T}$ Flows
• Fractal dimension of critical curves in the $O(n)$-symmetric ${\varphi }^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models
• Aspects of Hyperscaling Violating Geometries at Finite Cutoff
• Nonlinear automorphism of the conformal algebra in 2D and continuous $\sqrt{T\bar{T}}$ deformations
• Non-Linear Supersymmetry and $T\bar{T}$-like Flows
• Random Boundary Geometry and Gravity Dual of $T\bar{T}$ Deformation
• $T\bar{T}$ in JT Gravity and BF Gauge Theory
• Infinite pseudo-conformal symmetries of classical $T\bar{T}$, $J\bar{T}$ and $J{T}_a$ - deformed CFTs
• Boundary conditions for General Relativity in three-dimensional spacetimes, integrable systems and the KdV/mKdV hierarchies
• Entanglement entropy and $T\bar{T}$ deformations beyond antipodal points from holography
• Interacting Chiral Form Field Theories and $T\overline{T}$-like Flows in Six and Higher Dimensions
• Non-relativistic duality and $T\bar{T}$ deformations
• $T\bar{T}$-deformed conformal field theories out of equilibrium
• Heating up holography for single-trace $J\bar{T}$ deformations
• 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
• Geometric formulation of generalized root-$T\bar{T}$ deformations
• Thermal transport in $T\bar{T}$-deformed conformal field theories: from integrability to holography
• Stress Tensor Flows, Birefringence in Non-Linear Electrodynamics, and Supersymmetry
• Root-$T\overline{T}$ Deformed Boundary Conditions in Holography
• Large $N$ phase transition in $T\overline{T}$-deformed $2d$ Yang-Mills theory on the sphere
• Massive gravity generalization of $T\overline{T}$ deformations
• Geometry and Complexity of Path Integrals in Inhomogeneous CFTs
• Glue-on AdS holography for $T\bar{T}$-deformed CFTs
• Geometrizing non-relativistic bilinear deformations
• $T\bar{T}$ deformation of chiral bosons and Chern-Simons AdS${}_3$ gravity
• $T\bar{T}$ Deformation of Stress-Tensor Correlators from Random Geometry
• Holographic torus correlators of stress tensor in $Ad{S}_3/CF{T}_2$
• $T\bar{T}$-flow effects on torus partition functions
• Matrix Theory Reloaded: A BPS Road to Holography
• Quantum corrections to finite radius holography and holographic entanglement entropy
• $T\overline{T}$ deformations of non-Lorentz invariant field theories
• TsT, black holes, and $T\bar{T}+J\bar{T}+T\bar{J}$
• $T\bar{T}$ flow as characteristic flows
• Very Special $T\bar{J}$ deformed CFT
• Gluing AdS/CFT
• Thermodynamic Bethe Ansatz past turning points: the (elliptic) sinh-Gordon model
• Building Tensor Networks for Holographic States
• The Space of Integrable Systems from Generalised $T\bar{T}$-Deformations
• $T\overline{T}$ Deformations of Supersymmetric Quantum Mechanics
• S-duality in $T\bar{T}$-deformed CFT
• Confining Strings, Infinite Statistics and Integrability
• $T\bar{T}$-deformation and Liouville gravity
• Quantization of the ModMax Oscillator
• Exact $T\bar{T}$-deformation of two-dimensional Yang-Mills theory on the sphere
• Topological Gauging and Double Current Deformations
• Baby Universes and Worldline Field Theories
• $T\overline{T}$-Like Flows and $3d$ Nonlinear Supersymmetry
• A Path Integral Realization of Joint $J\bar{T}$, $T\bar{J}$ and $T\bar{T}$ Flows
• Holographic study of $T\bar{T}$ like deformed HV QFTs: holographic entanglement entropy
• $T\bar{T}$ deformation of the Ising model and its ultraviolet completion
• Lax Connections in $T\bar{T}$-deformed Integrable Field Theories
• $T\bar{T}$ deformed YM${}_2$ on general backgrounds from an integral transformation
• A general definition of $J{T}_a$ -- deformed QFTs
• On the classification of UV completions of integrable $T\bar{T}$ deformations of CFT
• Thermodynamics of $T\bar{T}$, $J\bar{T}$, $T\bar{J}$ deformed conformal field theories
• Krylov complexity of deformed conformal field theories
• Flows in the Space of Interacting Chiral Boson Theories
• On the universal behavior of $T\bar{T}$-deformed CFTs: single and double-trace partition functions at large $c$
• $T\bar{T}$ deformation on multiquantum mechanics and regenesis
• $T\overline{T}$ Deformations of nonrelativistic models
• $T\bar{T}/J\bar{T}$-deformed WZW models from Chern-Simons AdS${}_3$ gravity with mixed boundary conditions
• $T\overline{T}$-deformation of $q$-Yang-Mills theory
• Deforming the ODE/IM correspondence with $\mathrm{T}\bar{\mathrm{T}}$
• Large N Analysis of $T\bar{T}$-deformation and Unavoidable Negative-norm States
• Surface charges in Chern-Simons gravity with $T\bar{T}$ deformation
• Exact $T\overline{T}$ deformation of two-dimensional Maxwell theory
• $T\bar{T}+{\Lambda }_2$ from a 2d gravity path integral
• Traversable AdS Wormhole via Non-local Double Trace or Janus Deformation
• Holographic Dual of Conformal Field Theories with Very Special $T\bar{J}$ Deformations
• Remarks on the thermodynamic stability of TT-bar deformations
• Irrelevant Deformations with Boundaries and Defects
• On the $T\bar{T}$ deformation of the compactified boson and its interpretation in Lattice Gauge Theory
• Perturbative renormalization of the $T\bar{T}$-deformed free massive Dirac fermion
• Confining strings in three-dimensional gauge theories beyond the Nambu--Gotō approximation
• Freelance Holography, Part II: Moving Boundary in Gauge/Gravity Correspondence
• Geodesic geometry of 2+1-D Dirac materials subject to artificial, quenched gravitational singularities
• Emergent dual holographic description for interacting Dirac fermions in the large $N$ limit
• Emergent dual holographic description as a non-perturbative generalization of the Wilsonian renormalization group
• Renyi divergences from Euclidean quenches
• Symmetries versus the spectrum of $J\bar{T}$-deformed CFTs
• Thermodynamics of $T\bar{T}$ perturbations of some single particle field theories
• Supersymmetric black holes and $T\bar{T}$ deformation
• Aspects of $T\bar{T}+J\bar{T}$ deformed Schwarzian: From gravity partition function to late-time spectral form factor
• One-loop partition functions in $T\overline{T}$-deformed AdS${}_3$
• Quantization of the Zigzag Model
• Gravitational perturbations as $T\bar{T}$-deformations in 2D dilaton gravity systems
• Entanglement transfer from quantum matter to classical geometry in an emergent holographic dual description of a scalar field theory
• Chiral Decoupling from Irrelevant Deformations
• Weighed average over Narain moduli space as $T\bar{T}$ deformation of CFT target space
• Holographic Entanglement Entropy in $T\bar{T}$-deformed CFTs
• The phase diagram of $T\bar{T}$-deformed Yang-Mills theory on the sphere
• $T\bar{T}$ deformation of correlation functions
• Holographic n-partite Information in Hyperscaling Violating Geometry
• $T\bar{T}$ Deformations in Curved Space from 4D Chern-Simons Theory
• Composite operators in $T\bar{T}$-deformed free QFTs
• Holographic boundary conformal field theory with $T\bar{T}$ deformation
• Systematic approach to correlators in $T\bar{T}$ deformed CFTs
• Geometric realization via irrelevant deformations induced by the stress-energy tensor
• Note on higher-point correlation functions of the $T\bar{T}$ or $J\bar{T}$ deformed CFTs
• Nonequilibrium thermodynamics perspectives for the monotonicity of the renormalization group flow
• On the symmetry of $T\bar{T}$ deformed CFT
• Characters of irrelevant deformations
• Root-$T\overline{T}$ deformed CFT partition functions at large central charge
• Soliton, breather and shockwave solutions of the Heisenberg and the $T\bar{T}$ deformations of scalar field theories in 1+1 dimensions
• Nonperturbative aspects of two-dimensional $T\bar{T}$-deformed scalar theory from functional renormalization group
• A substrate for brane shells from $T\bar{T}$
• On Factorizable S-matrices, Generalized TTbar, and the Hagedorn Transition
• $T\bar{T}$ deformed scattering happens within matrices
• Renormalization group flow to effective quantum mechanics at IR in an emergent dual holographic description for spontaneous chiral symmetry breaking
• Loop corrections versus marginal deformation in celestial holography
• Geometric realization of stress-tensor deformed field theory
• Phase Transition in JT Gravity and $T\bar{T}$ Deformation
• Monotonicity of RG flow in emergent dual holography of worldsheet nonlinear $\sigma$ model
• A $T\bar{T}$-like deformation of the Skyrme model and the Heisenberg model of nucleon-nucleon scattering
• On the Spread of Entanglement at Finite Cutoff
• On correlators in $T\bar{T}$-deformed conformal field theories
• Burgers Equation vs. Large $N$ Limit in $T\bar{T}$-deformed $O(N)$ Vector Model
• The on-shell action of supergravity & the B-side of TsT and single-trace $T\bar{T}$
• On Current-Squared Flows and ModMax Theories
• Metric approach to a $\mathrm{T}\bar{\mathrm{T}}-$like deformation in arbitrary dimensions