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

TL;DR

This work develops a principled method to construct minimal form factors for integrable quantum field theories perturbed by TTbar-like irrelevant operators. By extending the integral representation of the logarithm of the minimal form factor and, separately, by an adapted Karowski-Weisz contour approach, the authors fix the previously free beta parameters and obtain a parameter-free, UV-consistent MFF factor D_alpha that multiplies the undeformed MFF F_min(theta). They demonstrate TTbar-like deformations for the Ising theory and for TTbar_{2n-1}-type perturbations, deriving explicit delta(theta) and rho(theta) structures and revealing a critical alpha_c beyond which the MFF behavior near theta=0 changes qualitatively. The results clarify the interplay between analyticity, asymptotics, and locality in TTbar-perturbed IQFTs and illuminate how correlation functions and higher-particle form factors may behave in these deformed theories, while also pointing to potential breakdowns of the standard form factor program in the presence of nontrivial CDD factors. Practical impact includes providing a concrete, well-behaved framework for computing correlators in TTbar-deformed IQFTs and guiding future exploration of non-factorized solutions and locality considerations in this broader class of models.

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.

Figures (5)

• Figure 1: Comparison of MFFs with the inclusion of $\cosh$ terms, for $\alpha$ positive and negative, on different lines ${\rm Im}\eta = 0,-\frac{1}{4},-\frac{1}{2},-\frac{3}{4},-1$.
• Figure 2: Comparison of MFFs with and without the inclusion of $\cosh$ terms on the line $\eta \in \mathbb{R}$ (i.e. ${\rm Im}\theta = i\pi$).
• Figure 3: Comparison of MFFs with and without the inclusion of $\cosh$ terms on the line $\theta \in \mathbb{R}$.
• Figure 4: Plots of the MFF obtained from \ref{['eq:TTb_Ising_mff']} as a function of $\theta\in\mathbb{R}$ for various values of $\alpha >0$.
• Figure 5: The contour $C$ in equation (\ref{['KW1']}).