On Intersecting Conformal Defects

Abstract

We study the physics of 2 and 3 mutually intersecting conformal defects forming wedges and corners in general dimension. For 2 defects we derive the beta function of the edge interactions for infinite and semi-infinite wedges and study them in the tricritical model in $d=3-\epsilon$ as an example. We discuss the dependency of the edge anomalous dimension on the intersection angle, connecting to an old issue known in the literature. Additionally, we study trihedral corners formed by 3 planes and compute the corner anomalous dimension, which can be considered as a higher-dimensional analog of the cusp anomalous dimension. We also study 3-line corners related to the three-body potential of point-like impurities.