A general definition of $JT_a$ -- deformed QFTs

TL;DR

This paper introduces a path-integral framework for 2D quantum field theories deformed by an integrable, irrelevant operator, revealing their geometric flow, S-matrix phase modification, and UV completeness, especially in integrable cases.

Contribution

It provides a general path-integral definition for deformed 2D QFTs using gauge fields and vielbeins, connecting geometric flow equations with energy spectrum changes.

Findings

Partition function satisfies a geometric flow equation.

Deformed S-matrix differs by a phase factor depending on charges and momenta.

Phase factor reproduces finite-size spectrum shifts in integrable models.

Abstract

We propose a general path-integral definition of two-dimensional quantum field theories deformed by an integrable, irrelevant vector operator constructed from the components of the stress tensor and those of a $U(1)$ current. The deformed theory is obtained by coupling the original QFT to a flat dynamical gauge field and "half" a flat dynamical vielbein. The resulting partition function is shown to satisfy a geometric flow equation, which perfectly reproduces the flow equations for the deformed energy levels that were previously derived in the literature. The S-matrix of the deformed QFT differs from the original S-matrix only by an overall phase factor that depends on the charges and momenta of the external particles, thus supporting the conjecture that such QFTs are UV complete, although intrinsically non-local. For the special case of an integrable QFT, we check that this phase factor precisely reproduces the change in the finite-size spectrum via the Thermodynamic Bethe Ansatz equations.