Reflection and Transmission for Conformal Defects

TL;DR

The paper introduces two defect observables, $\mathcal{R}$ and $\mathcal{T}$, that quantify the reflectivity and transmissivity of conformal defects between CFTs, defined via boundary-state data and stress-tensor correlators with the folded theory formalism. It proves basic properties, including $\mathcal{R}+\mathcal{T}=1$ and invariance under the action of topological defects, and computes these quantities across a broad set of models: free boson/Ising, coset constructions, and minimal-model products. In unitary theories, $\mathcal{R},\mathcal{T}$ lie in $[0,1]$, while non-unitary examples demonstrate values outside this range, illustrating rich and sometimes counterintuitive transmission/reflection behavior of defects. The framework provides tools for classifying defects, analyzing defect RG flows, and understanding connections to generalized permutation branes in product CFTs.

Abstract

We consider conformal defects joining two conformal field theories along a line. We define two new quantities associated to such defects in terms of expectation values of the stress tensors and we propose them as measures of the reflectivity and transmissivity of the defect. Their properties are investigated and they are computed in a number of examples. We obtain a complete answer for all defects in the Ising model and between certain pairs of minimal models. In the case of two conformal field theories with an enhanced symmetry we restrict ourselves to non-trivial defects that can be obtained by a coset construction.