Bosonic-type S-Matrix, Vacuum Instability and CDD Ambiguities
G. Mussardo, P. Simon
TL;DR
The paper investigates the simplest bosonic-type $S$-matrix, which is typically deemed unphysical due to complex finite-volume energies, and argues for its interpretation as a massive Ising model perturbed by irrelevant operators. Through Thermodynamic Bethe Ansatz and Form Factor analyses, it demonstrates ultraviolet instabilities and ambiguities in the form-factor program, signaling a breakdown of standard QFT interpretation. The authors relate the bosonic $S$-matrix to CDD-factor deformations of a fermionic baseline and show that such deformations correspond to adding irrelevant operators that can destabilize the vacuum, yielding a nonlocal and ill-defined UV behavior. This study highlights the delicate interplay between $S$-matrix data, perturbations of conformal fixed points, and the existence of a consistent ultraviolet completion. The findings emphasize that, even for integrable models, knowledge of the $S$-matrix alone may be insufficient to guarantee a well-defined underlying quantum field theory.
Abstract
We consider the simplest bosonic-type S-matrix which is usually regarded as unphysical due to the complex values of the finite volume ground state energy. While a standard quantum field theory interpretation of such a scattering theory is precluded, we argue that the physical situation described by this S-matrix is of a massive Ising model perturbed by a particular set of irrelevant operators. The presence of these operators drastically affects the stability of the original vacuum of the massive Ising model and its ultraviolet properties.