Thermal transport in $T\bar{T}$-deformed conformal field theories: from integrability to holography

Abstract

In this paper we consider the energy and momentum transport in (1+1)-dimension conformal field theories (CFTs) that are deformed by an irrelevant operator $T\bar{T}$, using the integrability based generalized hydrodynamics, and holography. The two complementary methods allow us to study the energy and momentum transport after the in-homogeneous quench, derive the exact non-equilibrium steady states (NESS) and calculate the Drude weights and the diffusion constants. Our analysis reveals that all of these quantities satisfy universal formulae regardless of the underlying CFT, thereby generalizing the universal formulae for these quantities in pure CFTs. As a sanity check, we also confirm that the exact momentum diffusion constant agrees with the conformal perturbation. These fundamental physical insights have important consequences for our understanding of the $T\bar{T}$-deformed CFTs. First of all, they provide the first check of the $T\bar{T}$-deformed ${\mathrm{AdS}}_3$/${\mathrm{CFT}}_2$ correspondence from the dynamical standpoint. And secondly, we are able to identify a remarkable connection between the $T\bar{T}$-deformed CFTs and reversible cellular automata.

arXiv commentv1: 18 pages, 3 figures. v2: 20 pages, 3 figures, substantially improved results including a general derivation of the momentum diffusion constant. v3: Fig. 1 corrected, explanations improved. Published version

References in corpus (64)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence
• Shear viscosity of strongly coupled N=4 supersymmetric Yang-Mills plasma
• Hydrodynamics with Triangle Anomalies
• Structure Constants and Conformal Bootstrap in Liouville Field Theory
• Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
• On space of integrable quantum field theories
• Emergent hydrodynamics in integrable quantum systems out of equilibrium
• $T\bar{T}$-deformed 2D Quantum Field Theories
• Entanglement and thermodynamics after a quantum quench in integrable systems
• Integrable Structure of Conformal Field Theory, Quantum KdV Theory and Thermodynamic Bethe Ansatz
• Generalized HydroDynamics on an Atom Chip
• Hydrodynamic Diffusion in Integrable Systems
• Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems
• Asymptotic Fragility, Near $Ad{S}_2$ Holography and $T\bar{T}$
• Solving the Simplest Theory of Quantum Gravity
• Three-dimensional quantum geometry and black holes
• Universal theory of nonlinear Luttinger liquids
• Cutoff AdS${}_3$ versus the $T\bar{T}$ deformation
• The $T\overline{T}$ deformation of quantum field theory as random geometry
• Diffusion in generalized hydrodynamics and quasiparticle scattering
• $T\bar{T}$ Partition Function from Topological Gravity
• Large-scale description of interacting one-dimensional Bose gases: generalized hydrodynamics supersedes conventional hydrodynamics
• Microscopic origin of ideal conductivity in integrable quantum models
• Conformal field theory out of equilibrium: a review
• Kinetic equation for a dense soliton gas
• Lecture notes on Generalised Hydrodynamics
• Electron Spin Resonance in S=1/2 antiferromagnetic chains
• Energy flow in non-equilibrium conformal field theory
• An integrable Lorentz-breaking deformation of two-dimensional CFTs
• Entanglement Scrambling in 2d Conformal Field Theory
• Dynamics of hard rods with initial domain wall state
• The $\text{T}\bar{\text{T}}$ perturbation and its geometric interpretation
• Operator Entanglement in Interacting Integrable Quantum Systems: the Case of the Rule 54 Chain
• Drude Weight for the Lieb-Liniger Bose Gas
• A theory of reparameterizations for AdS${}_3$ gravity
• $T\bar{T}$ and the mirage of a bulk cutoff
• Diffusive hydrodynamics from integrability breaking
• On Correlation Functions for Non-critical Strings with c<1 but d>1
• Operator growth and eigenstate entanglement in an interacting integrable Floquet system
• Thermalisation of a trapped one-dimensional Bose gas via diffusion
• The effect of atom losses on the distribution of rapidities in the one-dimensional Bose gas
• Algebraic construction of current operators in integrable spin chains
• Current operators in Bethe Ansatz and Generalized Hydrodynamics: An exact quantum/classical correspondence
• Effective Action for Relativistic Hydrodynamics: Fluctuations, Dissipation, and Entropy Inflow
• The TT* deformation at large central charge
• Integrable many-body quantum Floquet-Thouless pumps
• On the Thermodynamic Bethe Ansatz Equation in Sinh-Gordon Model
• A hydrodynamic approach to non-equilibrium conformal field theories
• The Ubiquitous 'c': from the Stefan-Boltzmann Law to Quantum Information
• Equations of state in generalized hydrodynamics
• The collision rate ansatz for the classical Toda lattice
• Flow equations for generalised $T\bar{T}$ deformations
• Collision rate ansatz for quantum integrable systems
• Causality and the AdS Dirichlet problem
• Hydrodynamics of nonintegrable systems from a relaxation-time approximation
• Time-dependent matrix product ansatz for interacting reversible dynamics
• KdV charges in $T\bar{T}$ theories and new models with super-Hagedorn behavior
• Non-Equilibrium Conformal Field Theories with Impurities
• $T\bar{T}$-deformed conformal field theories out of equilibrium
• Diffusion from Convection
• Low temperature dynamics of nonlinear Luttinger liquids

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• A pedagogical review on solvable irrelevant deformations of 2d quantum field theory
• Correlation functions and transport coefficients in generalised hydrodynamics
• Rule 54: Exactly solvable model of nonequilibrium statistical mechanics
• Fragmentation and emergent integrable transport in the weakly tilted Ising chain
• $T\bar{T}$-deformed conformal field theories out of equilibrium
• Integrable hard rod deformation of the Heisenberg spin chains
• Gravity and $T\bar{T}$ flows in higher dimensions
• $\mathrm{T}\overline{\mathrm{T}}$-deformed 1d Bose gas
• Steady States of Holographic Interfaces
• Holographic study of $T\bar{T}$ like deformed HV QFTs: holographic entanglement entropy
• Integrable deformations of superintegrable quantum circuits
• An integrable spin chain with Hilbert space fragmentation and solvable real time dynamics
• $T\overline{T}$ deformations and the width of fundamental particles
• Universal thermalization dynamics in (1+1)d QFTs