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.

arXiv commentA section added, published version, 98 pages

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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
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• 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
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• $\mathrm{T}\overline{\mathrm{T}}$-deformed 1d Bose gas
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• $T\bar{T}$-flow effects on torus partition functions
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• $T\overline{T}$ Deformations of Supersymmetric Quantum Mechanics
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• Surface charges in Chern-Simons gravity with $T\bar{T}$ deformation
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• Traversable AdS Wormhole via Non-local Double Trace or Janus Deformation
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