$T\bar{T}$ Deformations and Form Factor Program

TL;DR

This paper reviews a method to compute minimal form factors in $T\bar{T}$-perturbed integrable field theories, generalizing standard techniques to include deformed scattering amplitudes and analyzing the emergence of poles.

Contribution

It introduces a generalized approach to compute minimal form factors in $T\bar{T}$-deformed theories, accounting for deformed scattering and pole structures.

Findings

The new form factors are products of undeformed solutions and a new function.

The new function is fixed by asymptotics, smoothness, and known limits.

Poles at zero rapidity can emerge and are analyzed within the integral representation.

Abstract

In this proceeding contribution, we review a recently proposed method to compute the minimal form factors (MFFs) of diagonal integrable field theories perturbed by irrelevant fields of the $T\bar{T}$ family. Our construction generalizes standard form factor techniques to deal with the deformed two-body scattering amplitudes, which are typical in this setting. The results are minimal form factors which are the product of the undeformed solution and a new function. This function can be fixed by requiring constant asymptotics for large rapidities, smoothness in the limit when the perturbation parameters go to zero, and agreement with standard MFF formulae for particular choices of the perturbation couplings. We observe that, for a certain range of parameters, the new MFF develops a pole at $\theta=0$. By considering several UV-complete theories, we argue that such poles can emerge naturally from the MFF integral representation and suggest how they may be eliminated.