On the RG Flow in the Two-Dimensional Coset Models

TL;DR

This paper investigates the renormalization group flow in two-dimensional coset models, constructing relevant fields and calculating correlation functions to understand field mixing between UV and IR regimes.

Contribution

It introduces a recursive method to construct perturbing and near-marginal fields, enabling calculation of structure constants and correlation functions in the model.

Findings

Explicit structure constants and four-point functions at leading order

Computed mixing coefficients between UV and IR fields

Provided a framework for analyzing RG flows in coset models

Abstract

We consider a RG flow in a general $\hat{su}(2)$ coset model perturbed by the least relevant field. The perturbing field as well as some particular fields of dimension close to one are constructed recursively in terms of lower level fields. Using this construction we obtain the structure constants and the four-point correlation functions in the leading order. This allows us to compute the mixing coefficients among the fields in the UV and the IR theory.