Spinning operators and defects in conformal field theory

TL;DR

This paper introduces a new method for constructing tensor structures in conformal field theories, enabling explicit computation of correlation functions involving operators and defects, and provides techniques for calculating conformal blocks in various channels.

Contribution

It presents a novel approach for constructing tensor structures in CFTs and offers explicit formulas for conformal blocks with defects, applicable to arbitrary bosonic representations.

Findings

New tensor structure construction method for primary operators.

Explicit formulas for conformal blocks in bulk and defect channels.

Techniques for generating conformal blocks via radial expansion and differential operators.

Abstract

We study the kinematics of correlation functions of local and extended operators in a conformal field theory. We present a new method for constructing the tensor structures associated to primary operators in an arbitrary bosonic representation of the Lorentz group. The recipe yields the explicit structures in embedding space, and can be applied to any correlator of local operators, with or without a defect. We then focus on the two-point function of traceless symmetric primaries in the presence of a conformal defect, and explain how to compute the conformal blocks. In particular, we illustrate various techniques to generate the bulk channel blocks either from a radial expansion or by acting with differential operators on simpler seed blocks. For the defect channel, we detail a method to compute the blocks in closed form, in terms of projectors into mixed symmetry representations of the orthogonal group.