Integrable perturbations of CFT with complex parameter: the $M_{3/5}$ model and its generalizations

TL;DR

This paper investigates the dual massive and massless behaviors in the $ ext{M}_{3,5}$ non-unitary minimal model's $ ext{phi}_{2,1}$ perturbation using the Thermodynamic Bethe Ansatz, revealing new insights into non-unitary minimal models.

Contribution

It demonstrates the existence of both massive and massless regimes in non-unitary minimal models' perturbations by employing the TBA approach, extending understanding to a broader class of models.

Findings

Evidence of dual behaviors in the $ ext{M}_{3,5}$ model's perturbation.

Identification of a cascade of flows in non-unitary minimal models.

Connections established with the Izergin-Korepin model.

Abstract

We give evidence, by use of the Thermodynamic Bethe Ansatz approach, of the existence of both massive and massless behaviours for the $\phi_{2,1}$ perturbation of the $M_{3,5}$ non-unitary minimal model, thus resolving apparent contradictions in the previous literature. The two behaviours correspond to changing the perturbing bare coupling constant from real values to imaginary ones. Generalizations of this picture to the whole class of non-unitary minimal models $M_{p,2p\pm 1}$, perturbed by their least relevant operator lead to a cascade of flows similar to that of unitary minimal models perturbed by $\phi_{1,3}$. Various aspects and generalizations of this phenomenon and the links with the Izergin-Korepin model are discussed.