T T ¯ $$ \mathrm{T}\overline{\mathrm{T}} $$ -deformed 2D quantum field theories

Abstract

It was noticed many years ago, in the framework of massless RG flows, that the irrelevant composite operator TT, built with the components of the energy-momentum tensor, enjoys very special properties in 2D quantum field theories, and can be regarded as a peculiar kind of integrable perturbation. Novel interesting features of this operator have recently emerged from the study of effective string theory models.In this paper we study further properties of this distinguished perturbation. We discuss how it affects the energy levels and one-point functions of a general 2D QFT in finite volume through a surprising relation with a simple hydrodynamic equation. In the case of the perturbation of CFTs, adapting a result by Lüscher and Weisz we give a compact expression for the partition function on a finite-length cylinder and make a connection with the exact g-function method. We argue that, at the classical level, the deformation naturally maps the action of N massless free bosons into the Nambu-Goto action in static gauge, in N + 2 target space dimensions, and we briefly discuss a possible interpretation of this result in the context of effective string models.

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. A few comments about (2.4) are in order at this point:…”

“…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…”