On space of integrable quantum field theories

Abstract

We study deformations of 2D Integrable Quantum Field Theories (IQFT) which preserve integrability (the existence of infinitely many local integrals of motion). The IQFT are understood as "effective field theories", with finite ultraviolet cutoff. We show that for any such IQFT there are infinitely many integrable deformations generated by scalar local fields $X_s$, which are in one-to-one correspondence with the local integrals of motion; moreover, the scalars $X_s$ are built from the components of the associated conserved currents in a universal way. The first of these scalars, $X_1$, coincides with the composite field $(T\bar{T})$ built from the components of the energy-momentum tensor. The deformations of quantum field theories generated by $X_1$ are "solvable" in a certain sense, even if the original theory is not integrable. In a massive IQFT the deformations $X_s$ are identified with the deformations of the corresponding factorizable S-matrix via the CDD factor. The situation is illustrated by explicit construction of the form factors of the operators $X_s$ in sine-Gordon theory. We also make some remarks on the problem of UV completeness of such integrable deformations.

25 pages

References in corpus (5)

• $T\bar{T}$-deformed 2D Quantum Field Theories
• Solving the Simplest Theory of Quantum Gravity
• Expectation value of composite field $T\bar{T}$ in two-dimensional quantum field theory
• Fermionic structure in the sine-Gordon model: form factors and null-vectors
• Isomorphism of critical and off-critical operator spaces in two-dimensional quantum field theory

Cited by in corpus (53)

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• Marginal $T\bar{T}$-Like Deformation and ModMax Theories in Two Dimensions
• $T\bar{T}$-deformed conformal field theories out of equilibrium
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• Note on Rényi entropy of 2D perturbed free fermions
• Solving a family of $T\bar{T}$-like theories
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• Topological Gauging and Double Current Deformations
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• Thermodynamics of $T\bar{T}$, $J\bar{T}$, $T\bar{J}$ deformed conformal field theories
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• Time Evolution of Entanglement Entropy in Holographic FLRW Cosmologies
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• Irrelevant Deformations of Chiral Bosons
• Entanglement Entropy and Modular Hamiltonian of free fermion with deformations on a torus
• $T\bar{T}$-deformed 2D Yang-Mills at large N: collective field theory and phase transitions
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• Symmetries versus the spectrum of $J\bar{T}$-deformed CFTs
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• Non-equilibrium dynamics in Holography
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• Defining the $T\overline{T}$ Deformation on ${\mathrm{AdS}}_2$
• Canonical maps and integrability in $T\bar{T}$ deformed 2d CFTs
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