Boundary Flows in general Coset Theories

TL;DR

This paper investigates boundary effects in off-critical integrable coset conformal field theories, analyzing boundary flows, their lattice model interpretations, and applications to impurity screening in Kondo models using TBA methods.

Contribution

It introduces a detailed analysis of boundary flows in coset CFTs with integrable boundary conditions, verified through TBA and lattice model correspondence, including super CFTs and Kondo impurity models.

Findings

Boundary flows verified via TBA and boundary entropies.

Flows are consistent with lattice RSOS models and super CFTs.

Impurity screening in Kondo models modeled by taking specific limits.

Abstract

In this paper we study the boundary effects for off-critical integrable field theories which have close analogs with integrable lattice models. Our models are the $SU(2)_{k}\otimes SU(2)_{l}/SU(2)_{k+l}$ coset conformal field theories perturbed by integrable boundary and bulk operators. The boundary interactions are encoded into the boundary reflection matrix. Using the TBA method, we verify the flows of the conformal BCs by computing the boundary entropies. These flows of the BCs have direct interpretations for the fusion RSOS lattice models. For super CFTs ($k=2$) we show that these flows are possible only for the Neveu-Schwarz sector and are consistent with the lattice results. The models we considered cover a wide class of integrable models. In particular, we show how the the impurity spin is screened by electrons for the $k$-channel Kondo model by taking $l\to\infty$ limit. We also study the problem using an independent method based on the boundary roaming TBA. Our numerical results are consistent with the boundary CFTs and RSOS TBA analysis.