Renormalization group flows for the second $Z_{N}$ parafermionic field theory for N odd

TL;DR

This paper investigates how small perturbations affect the second $Z_{N}$ parafermionic field theory with odd N, identifying and classifying new fixed points using renormalization group, Coulomb gas, and coset methods.

Contribution

It introduces a novel analysis of the renormalization group flows for the second $Z_{N}$ parafermionic theory, revealing new fixed points and their classifications.

Findings

Discovery of new fixed points in the theory.

Classification of fixed points based on symmetry and perturbations.

Application of multiple techniques to analyze RG flows.

Abstract

Using the renormalization group approach, the Coulomb gas and the coset techniques, the effect of slightly relevant perturbations is studied for the second parafermionic field theory with the symmetry $Z_{N}$, for N odd. New fixed points are found and classified.