Correlators of Mixed Symmetry Operators in Defect CFTs

TL;DR

This paper systematically analyzes correlation functions of mixed symmetry operators in defect conformal field theories using the embedding formalism, providing explicit structures for various n-point functions and representations.

Contribution

It introduces a comprehensive method to compute invariant structures of correlation functions involving mixed symmetry operators in defect CFTs.

Findings

Derived all invariant structures for one-, two-, and three-point functions.

Generalized correlation functions to n-point cases.

Calculated correlation functions for operators in arbitrary $SO(q)$ representations.

Abstract

We use the embedding formalism to study correlation functions of a d-dimensional Euclidean CFT in the presence of a $q$ co-dimensional defect. The defect breaks the global conformal group $SO(d+1,1)$ into $SO(d-q+1,1) \times SO(q)$. We calculate all possible invariant structures that can appear in one-point, two-point and three-point correlation functions of bulk and defect operators in mixed symmetry representation. Their generalization to n-point correlation functions are also worked out. Correlation functions in the presence of a defect, in arbitrary representation of $SO(q)$, are also calculated.