Reflection and Transmission for Conformal Defects

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.Comment: 32 pages + 13 pages appendix, 12 figures; v2: added eqns (2.7), (2.8) and refs [6,7,39,40], version published in JHE