RG Domain Wall for the General su(2) Coset Models

TL;DR

This paper investigates renormalization group flows in general su(2) coset models induced by the least relevant field, comparing conformal perturbation theory and RG domain wall methods to verify consistent results.

Contribution

It introduces a novel comparison of two approaches for analyzing RG flows in su(2) coset models, confirming their agreement at leading order.

Findings

Matching mixing coefficients from both methods

Computed structure constants for the models

Validated the RG domain wall approach

Abstract

We consider a RG flow in a general su(2) coset model induced by the least relevant field. This is done using two different approaches. We first compute the mixing coefficients of certain fields in the UV and IR theories using a conformal perturbation theory. The necessary structure constants are computed. The same coefficients can be calculated using the RG domain wall construction of Gaiotto. We compute the corresponding one-point functions and show that the two approaches give the same result in the leading order.