Form Factors and Correlation Functions of $\mathrm{T}\overline{\mathrm{T}}$-Deformed Integrable Quantum Field Theories

TL;DR

This paper investigates how $ ext{T}ar{ ext{T}}$-deformations affect form factors and correlation functions in integrable quantum field theories, providing new insights into their short-distance behavior through the form factor program.

Contribution

It introduces the analysis of form factor equations under $ ext{T}ar{ ext{T}}$-perturbations, focusing on free theories and extending understanding of correlation functions in deformed integrable models.

Findings

Form factor equations admit general solutions under $ ext{T}ar{ ext{T}}$-deformations.

Deformations influence the short-distance behavior of correlation functions.

Results extend to some non-free theories, broadening applicability.

Abstract

The study of $\mathrm{T}\overline{\mathrm{T}}$-perturbed quantum field theories is an active area of research with deep connections to fundamental aspects of the scattering theory of integrable quantum field theories, generalised Gibbs ensembles, and string theory. Many features of these theories, such as the peculiar behaviour of their ground state energy and the form of their scattering matrices, have been studied in the literature. However, so far, very few studies have approached these theories from the viewpoint of the form factor program. From the perspective of scattering theory, the effects of a $\mathrm{T}\overline{\mathrm{T}}$ perturbation (and higher spin versions thereof) is encoded in a universal deformation of the two-body scattering matrix by a CDD factor. It is then natural to ask how these perturbations influence the form factor equations and, more generally, the form factor program. In this paper, we address this question for free theories, although some of our results extend more generally. We show that the form factor equations admit general solutions and how these can help us study the distinct behaviour of correlation functions at short distances in theories perturbed by irrelevant operators.