On Intersecting Conformal Defects

TL;DR

This paper investigates the behavior of intersecting conformal defects in various dimensions, deriving beta functions, anomalous dimensions, and exploring their dependence on intersection angles, with applications to models in different dimensions.

Contribution

It provides new analytical results on the beta functions and anomalous dimensions of intersecting conformal defects, including corners and wedges, in general dimensions.

Findings

Derived beta functions for edge interactions in wedge defects.

Calculated corner anomalous dimensions as higher-dimensional cusp analogs.

Analyzed the dependence of anomalous dimensions on intersection angles.

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.