New Integrable RG flows with Parafermions

TL;DR

This paper introduces new UV complete quantum field theories derived from RSOS scattering theories through specific irrelevant deformations, revealing a connection with parafermionic sinh-Gordon models and minimal CFTs.

Contribution

It identifies two novel UV complete QFTs linked to minimal CFTs, constructed via fine-tuned irrelevant deformations of RSOS theories, and confirms their properties through thermodynamic Bethe ansatz calculations.

Findings

Discovery of massless Z_{p-1} parafermionic sinh-Gordon models as UV completions.

Confirmation of the models via matching vacuum energies from TBA and quantization conditions.

Identification of a roaming trajectory connecting these theories to parafermionic minimal series.

Abstract

We consider irrelevant deformations of massless RSOS scattering theories by an infinite number of higher TTbar_{s+1} operators which introduce extra non-trivial CDD factors between left-movers and right-movers. It is shown that the resulting theories can be UV complete after bypassing typical Hagedorn-like singularities if the coefficients of the deformations are fine-tuned. In this way, we have discovered that only two new UV complete QFTs are associated with a M_p (p=3,4,...) minimal CFT based on the integrable structure of the RSOS scattering theory. One is the massless Z_{p-1} parafermionic sinh-Gordon models (PShG) with a self-dual coupling constant. This correspondence is confirmed by showing that the scale-dependent vacuum energies computed by the thermodynamic Bethe ansatz based on the S-matrices match those from the quantization conditions for the PShG models using the reflection amplitudes. The other UV QFT is reached from M_p by following the roaming trajectory of the Z_{p-1} parafermionic minimal series.