Expectation value of composite field $T\bar{T}$ in two-dimensional quantum field theory

Abstract

I show that the expectation value of the composite field $T\bar{T}$, built from the components of the energy-momentum tensor, is expressed exactly through the expectation value of the energy-momentum tensor itself. The relation is derived in two-dimensional quantum field theory under broad assumptions, and does not require integrability.

arXiv comment12 pages

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• $T\bar{T}$ deformed partition functions
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• Geometrizing $T\bar{T}$
• $T\bar{T}$, the entanglement wedge cross section, and the breakdown of the split property
• Aspects of Hyperscaling Violating Geometries at Finite Cutoff
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• Stress Tensor Flows, Birefringence in Non-Linear Electrodynamics, and Supersymmetry
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• Isomorphism of critical and off-critical operator spaces in two-dimensional quantum field theory
• Osborn Equation and Irrelevant Operators
• Form factors of descendant operators in the massive Lee-Yang model
• Holographic complexity for black branes with momentum relaxation
• $T\overline{T}$-Like Flows and $3d$ Nonlinear Supersymmetry
• Lax Connections in $T\bar{T}$-deformed Integrable Field Theories
• Freelance Holography, Part I: Setting Boundary Conditions Free in Gauge/Gravity Correspondence
• Comments on holographic entanglements in cutoff AdS
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• An integrable spin chain with Hilbert space fragmentation and solvable real time dynamics
• States, symmetries and correlators of $T\bar{T}$ and $J\bar{T}$ symmetric orbifolds
• Freelance Holography, Part II: Moving Boundary in Gauge/Gravity Correspondence
• $T\overline{T}$ deformations and the width of fundamental particles
• The complex sinh-Gordon model: form factors of descendant operators and current-current perturbations
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• $T\bar{T}$ deformation of correlation functions
• On the symmetry of $T\bar{T}$ deformed CFT
• Locality and Conserved Charges in $T\overline{T}$-Deformed CFTs
• On correlation functions in models related to the Temperley-Lieb algebra
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• Nonlocal charges from marginal deformations of 2D CFTs: Holographic $T\bar{T}$, $T\bar{J}$ and Yang-Baxter deformations
• A $T\bar{T}$-like deformation of the Skyrme model and the Heisenberg model of nucleon-nucleon scattering
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• Burgers Equation vs. Large $N$ Limit in $T\bar{T}$-deformed $O(N)$ Vector Model
• Exact summation of leading logs around $T\bar{T}$ deformation of $O(N+1)$-symmetric 2D QFTs