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.Comment: 25 page

T T ¯ $$ \mathrm{T}\overline{\mathrm{T}} $$ and LST

“…The coupling t must be taken to be positive for the theory to have a vacuum [4]. In the infrared limit t → 0, (2.4) approaches the standard CFT result, 5) corresponding to a state 1 with L 0 =L 0 = h. Equation (2.4) describes the change of the energy of such a state as we turn on the perturbation.…”

“…In section 2 we discuss some of the results of [4,5]. In particular, we point out that the spectrum of a CF T 2 on a spatial circle deformed by the irrelevant operator TT , interpolates between that of a CF T 2 at low energies and a spectrum with Hagedorn growth at high energies.…”

“…The aim of this note is to take advantage of recent progress in field theory [4,5] to (partially) rectify this situation. We will argue that a large class of two dimensional conformal field theories deformed by a certain single trace TT operator provide a boundary description of two dimensional vacua of LST.…”

“…In this section we discuss some aspects of the recent work [4,5] (see also [6,7]) on the theory obtained by deforming the Lagrangian of a two dimensional conformal field theory JHEP07(2017)122…”

“…The resulting theory approaches the original CFT at long distances, whereas at short distances one in general expects the theory to lose predictive power. The authors of [4,5] used techniques from integrable field theory to study the deformation (2.1). In particular, they calculated exactly the spectrum of the theory on a circle of circumference R and found it to be…”