On space of integrable quantum field theories

By F. Smirnov, A. Zamolodchikov. 2016

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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 XsXs, which are in one-to-one correspondence with the local integrals of motion; moreover, the scalars XsXs are built from the components of the associated conserved currents in a universal way. The first of these scalars, X1X1, coincides with the composite field View the MathML source(TT¯) built from the components of the energy-momentum tensor. The deformations of quantum field theories generated by X1X1 are "solvable" in a certain sense, even if the original theory is not integrable. In a massive IQFT the deformations XsXs 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 XsXs in sine-Gordon theory. We also make some remarks on the problem of UV completeness of such integrable deformations

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/3cc39fcb3f8127e24562df4b844fe19fbcef6a64

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Citations in the corpus

Holography at finite cutoff with a T2 deformation (2018, background): “The proposal in [8] is that 3d gravity at finite radial cutoff is dual to a 2d CFT deformed by the irrelevant operator T T̄ , a deformation previously studied in the field theory context by Zamolodchikov and Smirnov [9, 10].”
A theory of reparameterizations for AdS3 gravity (2018, background): “There has been a recent explosion of activity on the so-called T T̄ deformation of Zamolod- chikov and Smirnov [96, 97], including the question of its holographic dual (see e.g. [98]).”
Towards a 2d QFT analog of the SYK model (2017, background): “10), indicates that the leading order correction to the IR conformal field theory takes the form of an irrelevant T T̄ deformation, given by the product of the left- and right-moving stress tensors [29, 30, 31, 32].”
TT deformations in general dimensions (2018, neutral): “where we define S(0) as the CFT, which in turn implies that [1, 25] ∂En ∂λ + 2En ∂En ∂R = 0.”
Holography Beyond AdS (2017, background): “As mentioned in the introduction, part of the motivation for our work, here and in [1,2], is the results of [5,6] on TT deformed CFT2.”
A solvable irrelevant deformation of AdS3/CFT2 (2017, background): “In [1], we pointed out that there is a single trace deformation of string theory on AdS3 that shares many elements with that of [2,3], but may be more interesting, since it modifies the local geometry of the bulk theory.”
TT¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ T\overline{T} $$\end{document} -deformations in closed form (2018, methodology): “3) is derived in [11], where the absence of contact terms in the T T̄ composite operator is proven to follow from general assumptions.”
An integrable Lorentz-breaking deformation of two-dimensional CFTs (2017, methodology): “Introduction Recently, Smirnov and Zamolodchikov [1] have studied an infinite class of irrelevant deformations of integrable two-dimensional QFTs (IQFTs), of the general double-trace form”