Reflection and transmission of conformal perturbation defects

TL;DR

This paper studies how interfaces that implement renormalisation group flows between conformal fixed points in two dimensions reflect and transmit energy, using perturbation theory and exact models to compute and verify these properties.

Contribution

It provides a third-order perturbative calculation of reflection and transmission coefficients for RG interfaces and compares them with exact coset model constructions.

Findings

Perturbative coefficients computed up to third order.

Results agree with exact coset model constructions.

Enhanced understanding of RG interface properties in 2D CFTs.

Abstract

We consider reflection and transmission of interfaces which implement renormalisation group flows between conformal fixed points in two dimensions. Such an RG interface is constructed from the identity defect in the ultraviolet CFT by perturbing the theory on one side of the defect line. We compute reflection and transmission coefficients in perturbation theory to third order in the coupling constant and check our calculations against exact constructions of RG interfaces between coset models.