New Integrable RG flows with Parafermions

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.