Spinning conformal defects

TL;DR

This paper develops a formalism for analyzing conformal defects with spin, deriving recursion relations and methods to compute their correlation functions within the embedding space framework.

Contribution

It introduces a systematic approach to describe spinning conformal defects and their correlation functions, extending the embedding space formalism to include spin effects.

Findings

Derived integral representation of spinning defect OPE blocks.

Established recursion relations for defect correlation functions.

Constructed spinning defect correlators from scalar cases using differential operators.

Abstract

We consider conformal defects with spins under the rotation group acting on the transverse directions. They are described in the embedding space formalism in a similar manner to spinning local operators, and their correlation functions with bulk and defect local operators are determined by the conformal symmetry. The operator product expansion (OPE) structure of spinning conformal defects is examined by decomposing it into the spinning defect OPE block that packages all the contribution from a conformal multiplet. The integral representation of the block derived in the shadow formalism is facilitated to deduce recursion relations for correlation functions of two spinning conformal defects. In simple cases, we construct spinning defect correlators by acting differential operators recursively on scalar defect correlators.