$T\bar{T}$-deformed 2D Quantum Field Theories

Abstract

It was noticed many years ago, in the framework of massless RG flows, that the irrelevant composite operator $T\bar{T}$, built with the components of the energy-momentum tensor, enjoys very special properties in 2D quantum field theories, and can be regarded as a peculiar kind of integrable perturbation. Novel interesting features of this operator have recently emerged from the study of effective string theory models.In this paper we study further properties of this distinguished perturbation. We discuss how it affects the energy levels and one-point functions of a general 2D QFT in finite volume through a surprising relation with a simple hydrodynamic equation. In the case of the perturbation of CFTs, adapting a result by Lüscher and Weisz we give a compact expression for the partition function on a finite-length cylinder and make a connection with the exact $g$-function method. We argue that, at the classical level, the deformation naturally maps the action of $N$ massless free bosons into the Nambu-Goto action in static gauge, in $N+2$ target space dimensions, and we briefly discuss a possible interpretation of this result in the context of effective string models.

arXiv comment27 pages, 2 figures. v2: New references and comments included, minor typos corrected

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• An integrable Lorentz-breaking deformation of two-dimensional CFTs
• Holography at finite cutoff with a $T^2$ deformation
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• $T\bar{T}$-deformations in closed form
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• $T\bar{T}$ and the mirage of a bulk cutoff
• Holography Beyond AdS
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• Generalised Born-Infeld models, Lax operators and the $\text{T}\bar{\text{T}}$ perturbation
• Strings on NS-NS Backgrounds as Integrable Deformations
• A pedagogical review on solvable irrelevant deformations of 2d quantum field theory
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• $T\overline{T}$ in AdS${}_2$ and Quantum Mechanics
• Non-Equilibrium Dynamics and Weakly Broken Integrability
• $T\bar{T}$ and EE, with implications for (A)dS subregion encodings
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• Entanglement Entropy in $T\overline{T}$-Deformed CFT
• $T\bar{T}$ Deformations, Massive Gravity and Non-Critical Strings
• Hamiltonian deformations in quantum mechanics, $T\bar{T}$, and SYK
• The holographic interpretation of $J\bar{T}$-deformed CFTs
• On $T\bar{T}$ deformations and supersymmetry
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• $J\bar{T}$ deformed $CF{T}_2$ and String Theory
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• de Sitter Microstates from $T\bar{T}+{\Lambda }_2$ and the Hawking-Page Transition
• $T\bar{T}$ deformed CFT as a non-critical string
• Strings on warped AdS${}_3$ via $T\bar{J}$ deformations
• Correlation functions, entanglement and chaos in the $T\bar{T}$/$J\bar{T}$-deformed CFTs
• Conserved currents and $\text{T}{\bar{\text{T}}}_s$ irrelevant deformations of 2D integrable field theories
• Integrable Deformations of Sigma Models
• Root-$T\overline{T}$ Deformations in Two-Dimensional Quantum Field Theories
• Comments on wormholes, ensembles, and cosmology
• TsT, $T\bar{T}$ and black strings
• Sphere partition functions and cut-off AdS
• Integrable spin chain for stringy Wess-Zumino-Witten models
• Holographic integration of $T\bar{T}$ and $J\bar{T}$ via $O(d,d)$
• The TT* deformation at large central charge
• Entanglement Entropy for $TT$ deformed CFT in general dimensions
• Moving the CFT into the bulk with $T\bar{T}$
• Mapping relativistic to ultra/non-relativistic conformal symmetries in 2D and finite $\sqrt{T\bar{T}}$ deformations
• Comments on $T\bar{T}$ double trace deformations and boundary conditions
• 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
• $T\bar{T}$ Flows and (2,2) Supersymmetry
• Modular covariance and uniqueness of $J\bar{T}$ deformed CFTs
• Background independent holographic dual to $T\bar{T}$ deformed CFT with large central charge in 2 dimensions
• Structure Constants in $\mathcal{N}=4$ SYM at Finite Coupling as Worldsheet $g$-Function
• $T\bar{T}$ deformations and integrable spin chains
• Integrability and Renormalization under $T\bar{T}$
• Conformal field theory complexity from Euler-Arnold equations
• Conformal data and renormalization group flow in critical quantum spin chains using periodic uniform matrix product states
• $T\bar{T},J\bar{T}$, $T\bar{J}$ Partition Sums From String Theory
• $T\overline{T}$, $\tilde{J}J$, $JT$ and $\tilde{J}T$ deformations
• Complexity and Behind the Horizon Cut Off
• Quantum chaos, scrambling and operator growth in $T\bar{T}$ deformed SYK models
• Flow equations for generalised $T\bar{T}$ deformations
• Wilson loop in a $T\bar{T}$ like deformed ${\mathrm{CFT}}_2$
• Non-Hermitian Hamiltonian Deformations in Quantum Mechanics
• $T\bar{T}$ deformations as TsT transformations
• $T\bar{T}$-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
• Undressing Confining Flux Tubes with $T\bar{T}$
• Integrable S matrix, mirror TBA and spectrum for the stringy ${\text{AdS}}_3\times {\text{S}}^3\times {\text{S}}^3\times {\text{S}}^1$ WZW model
• Duality-Invariant Non-linear Electrodynamics and Stress Tensor Flows
• Holographic Entanglement Entropy in Cutoff AdS
• Expectation value of $\mathrm{T}\overline{\mathrm{T}}$ operator in curved spacetimes
• Gravitational path integral from the $T^2$ deformation
• Entanglement Wedge Reconstruction and the Information Paradox
• KdV charges in $T\bar{T}$ theories and new models with super-Hagedorn behavior
• $T\bar{T}$, the entanglement wedge cross section, and the breakdown of the split property
• Geometrizing $T\bar{T}$
• On the Classical Integrability of Root-$T\overline{T}$ Flows
• Aspects of Hyperscaling Violating Geometries at Finite Cutoff
• Nonlinear automorphism of the conformal algebra in 2D and continuous $\sqrt{T\bar{T}}$ deformations
• 3D Gravity in a Box
• Non-Linear Supersymmetry and $T\bar{T}$-like Flows
• Nonperturbative effects and resurgence in JT gravity at finite cutoff
• $T\bar{T}$ in JT Gravity and BF Gauge Theory
• Entanglement entropy and $T\bar{T}$ deformations beyond antipodal points from holography
• Boundary conditions for General Relativity in three-dimensional spacetimes, integrable systems and the KdV/mKdV hierarchies
• Infinite pseudo-conformal symmetries of classical $T\bar{T}$, $J\bar{T}$ and $J{T}_a$ - deformed CFTs
• Interacting Chiral Form Field Theories and $T\overline{T}$-like Flows in Six and Higher Dimensions
• $T\bar{T}+{\Lambda }_2$ Deformed CFT on the Stretched dS${}_3$ Horizon
• Field Theory of Interacting Boundary Gravitons
• 2D Ising Field Theory in a Magnetic Field: The Yang-Lee Singularity
• Non-relativistic duality and $T\bar{T}$ deformations
• Marginal $T\bar{T}$-Like Deformation and ModMax Theories in Two Dimensions
• $T\bar{T}$-deformed conformal field theories out of equilibrium
• A Non-Abelian Analogue of DBI from $T\overline{T}$
• Surface/State correspondence and $T\overline{T}$ deformation
• Finite Cutoff AdS${}_5$ Holography and the Generalized Gradient Flow
• Marginal deformations of WZW models and the classical Yang-Baxter equation
• Heating up holography for single-trace $J\bar{T}$ deformations
• Yang--Mills Glueballs as Closed Bosonic Strings
• 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
• $T\bar{T}$ Deformation and the Complexity=Volume Conjecture
• Geometric formulation of generalized root-$T\bar{T}$ deformations
• Integrable hard rod deformation of the Heisenberg spin chains
• $T\bar{T}$ type deformation in the presence of a boundary
• Geometric aspects of the ODE/IM correspondence
• Sequential Flows by Irrelevant Operators
• Thermal transport in $T\bar{T}$-deformed conformal field theories: from integrability to holography
• Note on Rényi entropy of 2D perturbed free fermions
• A Simple Worldsheet Black Hole
• S-matrix bootstrap for resonances
• Correlation Functions in $\text{T}\bar{\text{T}}$-deformed Conformal Field Theories
• Temporal Entanglement Entropy as a probe of Renormalization Group Flow
• Conformal Boundary Conditions from Cutoff AdS${}_3$
• Large $N$ phase transition in $T\overline{T}$-deformed $2d$ Yang-Mills theory on the sphere
• Massive gravity generalization of $T\overline{T}$ deformations
• Glue-on AdS holography for $T\bar{T}$-deformed CFTs
• Root-$T\overline{T}$ Deformed Boundary Conditions in Holography
• $\mathrm{T}\overline{\mathrm{T}}$-deformed 1d Bose gas
• Solving a family of $T\bar{T}$-like theories
• Stress Tensor Flows, Birefringence in Non-Linear Electrodynamics, and Supersymmetry
• Geometrizing non-relativistic bilinear deformations
• $T\bar{T}$ Deformation of Stress-Tensor Correlators from Random Geometry
• $T\bar{T}$ deformation of chiral bosons and Chern-Simons AdS${}_3$ gravity
• $T\bar{T}$-flow effects on torus partition functions
• TTbar deformation and the light-cone gauge
• Black hole to cosmic horizon microstates in string/M theory: timelike boundaries and internal averaging
• Spacetime as a quantum circuit
• Holography and Irrelevant Operators
• Matrix Theory Reloaded: A BPS Road to Holography
• Fix the dual geometries of $T\bar{T}$ deformed CFT${}_2$ and highly excited states of CFT${}_2$
• Supersymmetric $J\bar{T}$ and $T\bar{J}$ deformations
• TsT, black holes, and $T\bar{T}+J\bar{T}+T\bar{J}$
• $T\overline{T}$ deformations of non-Lorentz invariant field theories
• Chaos of QCD string from holography
• Quantum corrections to finite radius holography and holographic entanglement entropy
• Infinite Family of Integrable Sigma Models Using Auxiliary Fields
• The 2D Volkov-Akulov model as a $T\bar{T}$ deformation
• Gluing AdS/CFT
• Building Tensor Networks for Holographic States
• $T\bar{T}$ flow as characteristic flows
• More on Complexity in Finite Cut Off Geometry
• Very Special $T\bar{J}$ deformed CFT
• Thermodynamic Bethe Ansatz past turning points: the (elliptic) sinh-Gordon model
• S-duality in $T\bar{T}$-deformed CFT
• The Space of Integrable Systems from Generalised $T\bar{T}$-Deformations
• $T\overline{T}$ Deformations of Supersymmetric Quantum Mechanics
• Confining Strings, Infinite Statistics and Integrability
• $T\overline{T}$ deformation in SCFTs and integrable supersymmetric theories
• Homogeneous Yang-Baxter deformations as undeformed yet twisted models
• $T\bar{T}$-deformation and Liouville gravity
• Note on the nonrelativistic $T\bar{T}$ deformation
• Lifshitz Scaling, Microstate Counting from Number Theory and Black Hole Entropy
• Infinite $\mathrm{T}\bar{\mathrm{T}}$-like symmetries of compactified LST
• Topological Gauging and Double Current Deformations
• Extremal surfaces in glue-on AdS/$T\bar{T}$ holography
• Exact $T\bar{T}$-deformation of two-dimensional Yang-Mills theory on the sphere
• Maximally Supersymmetric RG Flows in 4D and Integrability
• $T\bar{T}$ deformation of the Ising model and its ultraviolet completion
• Holographic study of $T\bar{T}$ like deformed HV QFTs: holographic entanglement entropy
• Entropic c-functions in $T\bar{T},J\bar{T},T\bar{J}$ deformations
• $T\bar{T}$, $J\bar{T}$, $T\bar{J}$ and String Theory
• A Path Integral Realization of Joint $J\bar{T}$, $T\bar{J}$ and $T\bar{T}$ Flows
• $T\overline{T}$-Like Flows and $3d$ Nonlinear Supersymmetry
• Horizon symmetries and hairy black holes in AdS
• ModMax Oscillators and Root-$T\overline{T}$-Like Flows in Supersymmetric Quantum Mechanics
• End of the World Brane meets $T\bar{T}$
• A definition of primary operators in $J\bar{T}$-deformed CFTs
• A general definition of $J{T}_a$ -- deformed QFTs
• Classical Integrability of the Zigzag Model
• $T\bar{T}$ deformed YM${}_2$ on general backgrounds from an integral transformation
• Entanglement negativity in $\text{T}\bar{\text{T}}$-deformed CFT${}_2$s
• Lax Connections in $T\bar{T}$-deformed Integrable Field Theories
• $T\bar{T}$ and $J\bar{T}$ Deformations in Quantum Mechanics
• Sampling the lattice Nambu-Goto string using Continuous Normalizing Flows
• $T\bar{T}$ deformation on multiquantum mechanics and regenesis
• $T\overline{T}$-deformation of $q$-Yang-Mills theory
• 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
• Comments on holographic entanglements in cutoff AdS
• Krylov complexity of deformed conformal field theories
• $T\bar{T}/J\bar{T}$-deformed WZW models from Chern-Simons AdS${}_3$ gravity with mixed boundary conditions
• On the universal behavior of $T\bar{T}$-deformed CFTs: single and double-trace partition functions at large $c$
• Flows in the Space of Interacting Chiral Boson Theories
• KdV Charges and the Generalized Torus Partition Sum in $T\bar{T}$ deformation
• Entanglement Entropy for $T\bar{T}$, $J\bar{T}$, $T\bar{J}$ deformed holographic CFT
• $T\overline{T}$ Deformations of nonrelativistic models
• Emergent gravity from hidden sectors and TT deformations
• Universal flow equations and chaos bound saturation in 2d dilaton gravity
• Large N Analysis of $T\bar{T}$-deformation and Unavoidable Negative-norm States
• $T\bar{T}$ deformation of random matrices
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• Deforming the ODE/IM correspondence with $\mathrm{T}\bar{\mathrm{T}}$
• Surface charges in Chern-Simons gravity with $T\bar{T}$ deformation
• An integrable spin chain with Hilbert space fragmentation and solvable real time dynamics
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• Marginal quenches and drives in Tomonaga-Luttinger liquids
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• Remarks on the thermodynamic stability of TT-bar deformations
• Traversable AdS Wormhole via Non-local Double Trace or Janus Deformation
• Holographic Dual of Conformal Field Theories with Very Special $T\bar{J}$ Deformations
• Comments on $T\bar{T}$, $J\bar{T}$ and String Theory
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• Celestial amplitude for 2d theory
• Numerical determination of the width and shape of the effective string using Stochastic Normalizing Flows
• Irrelevant Deformations with Boundaries and Defects
• Time Evolution of Entanglement Entropy in Holographic FLRW Cosmologies
• Irrelevant Deformations of Chiral Bosons
• 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
• $T\bar{T}$ deformation of classical Liouville field theory
• Entanglement Entropy and Modular Hamiltonian of free fermion with deformations on a torus
• Renormalisation in $\text{T}\bar{\text{T}}$-Deformed (Non-)Integrable Theories
• Freelance Holography, Part II: Moving Boundary in Gauge/Gravity Correspondence
• $T\bar{T}$ deformed soft theorem
• Complexity via Replica Trick
• Non-linear Electrodynamics from Massive Gravity
• Time-dependent quantum correlations in two-dimensional expanding spacetime
• Exploring causality in braneworld/cutoff holography via holographic scattering
• Odd entanglement entropy in $\text{T}\bar{\text{T}}$ deformed CFT${}_2$s and holography
• $T\bar{T}$-deformed 2D Yang-Mills at large N: collective field theory and phase transitions
• Worldsheet traversable wormholes
• Irrelevant and marginal deformed BMS field theories
• One-loop partition functions in $T\overline{T}$-deformed AdS${}_3$
• $T\bar{T}$ and root-$T\bar{T}$ deformations in four-dimensional Chern-Simons theory
• Symmetries versus the spectrum of $J\bar{T}$-deformed CFTs
• Thermodynamics of $T\bar{T}$ perturbations of some single particle field theories
• Current-current deformations, conformal integrals and correlation functions
• $T\overline{T}$ deformations and the width of fundamental particles
• 4D Chern-Simons theory with auxiliary fields
• Renyi divergences from Euclidean quenches
• $J\bar{T}$-deformed CFTs as non-local CFTs
• Holographic $T\bar{T}$ deformation of the entanglement entropy in (A)dS${}_3$/CFT${}_2$
• $T\overline{T}$-deformed free energy of the Airy model
• Aspects of $T\bar{T}+J\bar{T}$ deformed Schwarzian: From gravity partition function to late-time spectral form factor
• Supersymmetric black holes and $T\bar{T}$ deformation
• Holographic entanglement entropy and mutual information in deformed field theories at finite temperature
• JT gravity at finite cutoff
• Chiral Decoupling from Irrelevant Deformations
• Warped Flatland
• Asymptotic Symmetries in the TsT/$T\bar{T}$ Correspondence
• Gravitational perturbations as $T\bar{T}$-deformations in 2D dilaton gravity systems
• Quantization of the Zigzag Model
• Bridging Boundaries: $T\bar{T}$, Double Holography, and Reflected Entropy
• Weighed average over Narain moduli space as $T\bar{T}$ deformation of CFT target space
• Holographic Complexity of LST and Single Trace $T\bar{T}$, $J\bar{T}$ and $T\bar{J}$ deformations
• Mixed state entanglement in deformed field theory at finite temperature
• Non-equilibrium dynamics in Holography
• The Generalised Born Oscillator and the Berry-Keating Hamiltonian
• The Algebraic Structure Underlying Pole-Skipping Points
• Momentum-space entanglement in scalar field theory on fuzzy spheres
• Correlation Functions in $\text{T}\bar{\text{T}}$-deformed Theories on the Torus
• Demystifying integrable QFTs in AdS: No-go theorems for higher-spin charges
• $T\bar{T}$ Deformations in Curved Space from 4D Chern-Simons Theory
• Bulk Spacetime Encoding via Boundary Ambiguities
• Composite operators in $T\bar{T}$-deformed free QFTs
• Solvable time-like cosets and holography beyond $AdS$
• $T\bar{T}$ deformation of correlation functions
• The Courant-Hilbert construction in 4D Chern-Simons theory
• Holographic boundary conformal field theory with $T\bar{T}$ deformation
• Critical Ising Model with Boundary Magnetic Field: RG Interface and Effective Hamiltonians
• The phase diagram of $T\bar{T}$-deformed Yang-Mills theory on the sphere
• $\frac{SL(2,\mathbb{R})\times U(1)}{U(1)}$ CFT, NS5$+$F1 system and single trace $T\bar{T}$
• Analytic integrability for holographic duals with $J\bar{T}$ deformations
• Systematic approach to correlators in $T\bar{T}$ deformed CFTs
• Integrable Lorentz-breaking deformations and RG flows
• On the symmetry of $T\bar{T}$ deformed CFT
• Note on higher-point correlation functions of the $T\bar{T}$ or $J\bar{T}$ deformed CFTs
• Geometric realization via irrelevant deformations induced by the stress-energy tensor
• From conformal correlators to analytic S-matrices: CFT${}_1$/QFT${}_2$
• Characters of irrelevant deformations
• Duality defect in a deformed transverse-field Ising model
• Mingling of the infrared and ultraviolet and the "cosmological constant" for interacting QFT in 2d
• On asymptotic behaviour in truncated conformal space approach
• Exact Renormalization of Wave Functionals yields Continuous MERA
• Deterministic Chaos vs Integrable Models
• 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
• Asymptotically Free AdS3/CFT2
• Complexity as a holographic probe of strong cosmic censorship
• Defining the $T\overline{T}$ Deformation on ${\mathrm{AdS}}_2$
• Canonical maps and integrability in $T\bar{T}$ deformed 2d CFTs
• Toward a Unified de Sitter Holography: A Composite $T\bar{T}$ and $T\bar{T}+{\Lambda }_2$ Flow
• Geometric realization of stress-tensor deformed field theory
• On Factorizable S-matrices, Generalized TTbar, and the Hagedorn Transition
• Phase Transition in JT Gravity and $T\bar{T}$ Deformation
• Comments on single trace $T\bar{T}$ and other current-current deformations
• Entanglement Renormalization of a $T\bar{T}$-deformed CFT
• On SYK traversable wormhole with imperfectly correlated disorders
• $T\bar{T}$ deformations and the pp wave correspondence
• $T\bar{T}$ deformation on non-Hermitian two coupled SYK model
• Comments on the negative specific heat of the $T\bar{T}$ deformed symmetric product CFT
• Nonperturbative aspects of two-dimensional $T\bar{T}$-deformed scalar theory from functional renormalization group
• $T\bar{T}$ deformed scattering happens within matrices
• Boundary Quantum Field Theories Perturbed by $\mathrm{T}\bar{\mathrm{T}}$: Towards a Form Factor Program
• Moving holographic boundaries
• Locality and Conserved Charges in $T\overline{T}$-Deformed CFTs
• A substrate for brane shells from $T\bar{T}$
• Exploring uberholography
• On exactly solvable Yang-Baxter models and enhanced symmetries
• Nonlocal charges from marginal deformations of 2D CFTs: Holographic $T\bar{T}$, $T\bar{J}$ and Yang-Baxter deformations
• Universal thermalization dynamics in (1+1)d QFTs
• Entanglement, defects, and $T\bar{T}$ on a black hole background
• Penrose limit for holographic duals of $J\bar{T}$ deformations
• $T\bar{T}$, Black Holes and Negative Strings
• A $T\bar{T}$-like deformation of the Skyrme model and the Heisenberg model of nucleon-nucleon scattering
• Field-Dependent Metrics and Higher-Form Symmetries in Duality-Invariant Theories of Non-Linear Electrodynamics
• Metric approach to a $\mathrm{T}\bar{\mathrm{T}}-$like deformation in arbitrary dimensions
• Krylov Complexity Under Hamiltonian Deformations and Toda Flows
• Cost of holographic path integrals
• The on-shell action of supergravity & the B-side of TsT and single-trace $T\bar{T}$
• Fine-tuning and the Second Law of Thermodynamics from the perspective of de Sitter quantum gravity
• $T\bar{T}$ deformation of Calogero-Sutherland model via dimensional reduction
• Scattering matrix for current-current deformations of the (2,2s+1) RSOS models
• On $\sqrt{T\overline{T}}$ deformed pathways: CFT to CCFT
• On String theory on deformed BTZ and $T\bar{T}+J\bar{T}+T\bar{J}$
• Constraints from Entanglement Wedge Nesting for Holography at a Finite Cutoff
• On the Spread of Entanglement at Finite Cutoff
• York time in JT gravity
• $\text{T}\bar{\text{T}}$-deformed Nonlinear Schrödinger
• Exact summation of leading logs around $T\bar{T}$ deformation of $O(N+1)$-symmetric 2D QFTs
• Burgers Equation vs. Large $N$ Limit in $T\bar{T}$-deformed $O(N)$ Vector Model
• On Current-Squared Flows and ModMax Theories