A pedagogical review on solvable irrelevant deformations of 2d quantum field theory

Abstract

This is a pedagogical review on $\mathrm{T}\overline{\mathrm{T}}$ deformation of two dimensional quantum field theories. It is based on three lectures which the author gave at ITP-CAS in December 2018. This review consists of four parts. The first part is a general introduction to $\mathrm{T}\overline{\mathrm{T}}$ deformation. Special emphasises are put on the deformed classical Lagrangian and the exact solvability of the spectrum. The second part focuses on the torus partition sum of the $\mathrm{T}\overline{\mathrm{T}}$/$\mathrm{J}\overline{\mathrm{T}}$ deformed conformal field theories and modular invariance/covariance. In the third part, different perspectives of $\mathrm{T}\overline{\mathrm{T}}$ deformation are presented, including its relation to random geometry, 2d topological gravity and holography. We summarize more recent developments until January 2021 in the last part.

A section added, published version, 98 pages

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• Conformal Boundary Conditions from Cutoff AdS${}_3$
• Geometrizing non-relativistic bilinear deformations
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• Building Tensor Networks for Holographic States
• More on Complexity in Finite Cut Off Geometry
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• $T\bar{T}$-deformation and Liouville gravity
• Strings, Symmetric Products, $T\bar{T}$ deformations and Hecke Operators
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• Large N Analysis of $T\bar{T}$-deformation and Unavoidable Negative-norm States
• Holographic Dual of Conformal Field Theories with Very Special $T\bar{J}$ Deformations
• Remarks on the thermodynamic stability of TT-bar deformations
• On the $T\bar{T}$ deformation of the compactified boson and its interpretation in Lattice Gauge Theory
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• Comments on D3-Brane Holography
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Cited by in corpus (63)

• Root-$T\overline{T}$ Deformations in Two-Dimensional Quantum Field Theories
• Non-Hermitian Hamiltonian Deformations in Quantum Mechanics
• Form factors and generalized hydrodynamics for integrable systems
• Boosting to BMS
• Duality-Invariant Non-linear Electrodynamics and Stress Tensor Flows
• Nonlinear automorphism of the conformal algebra in 2D and continuous $\sqrt{T\bar{T}}$ deformations
• $T\bar{T}$ in JT Gravity and BF Gauge Theory
• Interacting Chiral Form Field Theories and $T\overline{T}$-like Flows in Six and Higher Dimensions
• Field Theory of Interacting Boundary Gravitons
• Integrable hard rod deformation of the Heisenberg spin chains
• Geometric formulation of generalized root-$T\bar{T}$ deformations
• Correlation Functions in $\text{T}\bar{\text{T}}$-deformed Conformal Field Theories
• Temporal Entanglement Entropy as a probe of Renormalization Group Flow
• Massive gravity generalization of $T\overline{T}$ deformations
• $\mathrm{T}\overline{\mathrm{T}}$-deformed 1d Bose gas
• Stress Tensor Flows, Birefringence in Non-Linear Electrodynamics, and Supersymmetry
• $T\bar{T}$-flow effects on torus partition functions
• Matrix Theory Reloaded: A BPS Road to Holography
• $T\bar{T}$ flow as characteristic flows
• $T\overline{T}$ deformation in SCFTs and integrable supersymmetric theories
• $T\overline{T}$ Deformations of Supersymmetric Quantum Mechanics
• Holographic entanglement entropy in $T\overline{T}$-deformed AdS${}_3$
• Extremal surfaces in glue-on AdS/$T\bar{T}$ holography
• Topological Gauging and Double Current Deformations
• Maximally Supersymmetric RG Flows in 4D and Integrability
• Note on the nonrelativistic $T\bar{T}$ deformation
• ModMax Oscillators and Root-$T\overline{T}$-Like Flows in Supersymmetric Quantum Mechanics
• End of the World Brane meets $T\bar{T}$
• $T\overline{T}$ Deformations of nonrelativistic models
• Surface charges in Chern-Simons gravity with $T\bar{T}$ deformation
• $T\bar{T}$ deformation of random matrices
• $T\bar{T}+{\Lambda }_2$ from a 2d gravity path integral
• Traversable AdS Wormhole via Non-local Double Trace or Janus Deformation
• New classical integrable systems from generalized $T\bar{T}$-deformations
• Perturbative renormalization of the $T\bar{T}$-deformed free massive Dirac fermion
• Freelance Holography, Part II: Moving Boundary in Gauge/Gravity Correspondence
• Renormalisation in $\text{T}\bar{\text{T}}$-Deformed (Non-)Integrable Theories
• Exploring causality in braneworld/cutoff holography via holographic scattering
• Irrelevant and marginal deformed BMS field theories
• Holographic entanglement entropy and mutual information in deformed field theories at finite temperature
• Aspects of $T\bar{T}+J\bar{T}$ deformed Schwarzian: From gravity partition function to late-time spectral form factor
• 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
• One-loop partition functions in $T\overline{T}$-deformed AdS${}_3$
• Mixed state entanglement in deformed field theory at finite temperature
• Holographic Entanglement Entropy in $T\bar{T}$-deformed CFTs
• Krylov operator complexity in holographic CFTs: Smeared boundary reconstruction and the dual proper radial momentum
• Composite operators in $T\bar{T}$-deformed free QFTs
• $T\bar{T}$ Deformations in Curved Space from 4D Chern-Simons Theory
• Correlation Functions in $\text{T}\bar{\text{T}}$-deformed Theories on the Torus
• Geometric realization via irrelevant deformations induced by the stress-energy tensor
• Toward a Unified de Sitter Holography: A Composite $T\bar{T}$ and $T\bar{T}+{\Lambda }_2$ Flow
• Root-$T\overline{T}$ deformed CFT partition functions at large central charge
• Comments on the negative specific heat of the $T\bar{T}$ deformed symmetric product CFT
• A substrate for brane shells from $T\bar{T}$
• Nonperturbative aspects of two-dimensional $T\bar{T}$-deformed scalar theory from functional renormalization group
• The on-shell action of supergravity & the B-side of TsT and single-trace $T\bar{T}$
• Krylov Complexity Under Hamiltonian Deformations and Toda Flows
• On $\sqrt{T\overline{T}}$ deformed pathways: CFT to CCFT
• Exact summation of leading logs around $T\bar{T}$ deformation of $O(N+1)$-symmetric 2D QFTs
• Lecture notes on strings in AdS${}_3$ from the worldsheet and the AdS${}_3$/CFT${}_2$ duality
• $T\bar{T}$ deformation of Calogero-Sutherland model via dimensional reduction
• On Current-Squared Flows and ModMax Theories