Infrared Behaviour of Massless Integrable Flows entering the Minimal Models from phi_31

TL;DR

This paper investigates the infrared behavior of massless integrable flows entering minimal models from phi_31, revealing that two such flows are characterized by opposite coupling constants and analyzing their S matrices.

Contribution

It demonstrates that the two massless flows into minimal models have opposite phi_31 couplings, supported by TBA data and conformal perturbation theory comparisons.

Findings

The two flows have opposite phi_31 coupling constants.

TBA data aligns with conformal perturbation theory predictions.

Comments provided on the massless S matrices of these flows.

Abstract

It is known that any minimal model M_p receives along its phi_31 irrelevant direction *two* massless integrable flows: one from M_{p+1} perturbed by phi_{13}, the other from Z_{p-1} parafermionic model perturbed by its generating parafermion field. By comparing Thermodynamic Bethe Ansatz data and ``predictions'' of infrared Conformal Perturbation Theory we show that these two flows are received by M_p with opposite coupling constants of the phi_31 irrelevant perturbation. Some comments on the massless S matrices of these two flows are added.