Two Point Functions in Defect CFTs

TL;DR

This paper introduces a practical method for constructing two-point correlation functions in defect conformal field theories directly in physical space, handling arbitrary spins and providing explicit examples involving various fields.

Contribution

It offers an alternative to the embedding space formalism for two-point functions in defect CFTs, including methods for bulk-to-defect correlators and explicit example calculations.

Findings

Tabulated correlation functions involving conserved currents and energy-momentum tensors.

Analyzed constraints from conservation laws and equations of motion.

Provided explicit examples in free scalar and Maxwell theories.

Abstract

This paper is designed to be a practical tool for constructing and investigating two-point correlation functions in defect conformal field theory, directly in physical space, between any two bulk primaries or between a bulk primary and a defect primary, with arbitrary spin. Although geometrically elegant and ultimately a more powerful approach, the embedding space formalism gets rather cumbersome when dealing with mixed symmetry tensors, especially in the projection to physical space. The results in this paper provide an alternative method for studying two-point correlation functions for a generic $d$-dimensional conformal field theory with a flat $p$-dimensional defect and $d-p=q$ co-dimensions. We tabulate some examples of correlation functions involving a conserved current, an energy momentum tensor and a Maxwell field strength, while analysing the constraints arising from conservation and the equations of motion. A method for obtaining bulk-to-defect correlators is also explained. Some explicit examples are considered: free scalar theory on $\mathbb{R}^p \times ({\mathbb R}^q / {\mathbb Z}_2)$ and a free four dimensional Maxwell theory on a wedge.