Effective theory for fusion of conformal defects

TL;DR

This paper develops an effective field theory framework for understanding how conformal defects of any shape fuse in higher-dimensional conformal field theories, providing solutions to Weyl invariance constraints and exploring applications in cusp anomalous dimensions and defect anomalies.

Contribution

It introduces a comprehensive effective theory for defect fusion in conformal field theories, including solutions for arbitrary shapes and curved backgrounds, and analyzes defect anomalies and high-energy behaviors.

Findings

Solved Weyl invariance constraints for arbitrary defect shapes.

Derived high-energy asymptotics for bulk one-point functions.

Classified Weyl anomalies for defects breaking transverse rotations.

Abstract

We construct an effective field theory for fusion of conformal defects of any codimension in $d\geq 3$ conformal field theories. We fully solve the constraints of Weyl invariance for defects of arbitrary shape on general curved bulk manifolds and discuss the simplifications that arise for spherical defects on the conformal sphere. As applications, we study the structure of cusp anomalous dimensions in the anti-parallel lines limit and derive high-energy spin-dependent asymptotics for the one-point functions of bulk operators. We point out the potential importance of defects that break transverse rotations and initiate a classification of their Weyl anomalies.