Complete Minimal Form Factors for Irrelevant Deformations of Integrable Quantum Field Theory

TL;DR

This paper develops a method to compute minimal form factors for integrable quantum field theories with $T\bar{T}$ perturbations, addressing previous issues of free parameters and exploring the impact on form factor equations and asymptotic properties.

Contribution

It introduces a parameter-free construction of minimal form factors for perturbed theories, generalizing integral representations and analyzing their implications on form factor equations.

Findings

Derived parameter-free minimal form factors for $T\bar{T}$-perturbed theories.

Identified the limitations of unchanged form factor equations under perturbations.

Showed the necessity of modifying form factor equations to maintain analyticity and asymptotic properties.

Abstract

In this paper, we present a method to compute the minimal form factors (MFFs) of diagonal integrable field theories perturbed by generalized $T\bar{T}$ perturbations. Building on existing results by the same authors, these MFFs are constructed in such a way as not to allow for any free parameters, an issue that plagued previous solutions. The MFFs are derived from a generalization of the standard integral representation which has been used for UV-complete theories since the birth of the form factor bootstrap program. By UV-complete we mean theories whose short-distance/high-energy limit is a local conformal field theory. Their asymptotics is characterized by exponential decay at large rapidities. By computing higher particle form factors, we find that any natural higher-particle solutions involve the cancellation of parts of the newly found MFF. We conclude that the assumption that the form factor equations, particularly the kinematic residue equation, remain unchanged in the presence of $T\bar{T}$ perturbations, is too strong. There is a trade-off between having MFFs satisfying desirable analyticity and asymptotic properties and finding analytic solutions to the form factor equations, which is likely solved by nontrivial changes to the form factor equations, especially those where locality or semilocality of fields are essential assumptions.