Renormalization group flows for the second $\mathbb{Z}_{N}$ parafermionic field theory for $N$ even

TL;DR

This paper investigates the renormalization group flows in second $ ext{Z}_N$ parafermionic field theories for even N, revealing fixed points and flow structures similar to the odd N case, with new fixed points identified.

Contribution

It extends previous work on odd N to even N, analyzing perturbations and RG flows, and discovers additional fixed points in the theory.

Findings

RG equations exhibit similar structure for even and odd N

Identified fixed points corresponding to different models

Discovered new fixed point related to the (p-1)-th model

Abstract

Extending the results obtained in the case $N$ odd, the effect of slightly relevant perturbations of the second parafermionic field theory with the symmetry $\mathbb{Z}_{N}$, for $N$ even, are studied. The renormalization group equations, and their infra red fixed points exhibit the same structure in both cases. In addition to the standard flow from the $p$-th to the $(p-2)$-th model, another fixed point corresponding to the $(p-1)$-th model is found.