Conformal Blocks in Three Dimensions

TL;DR

This paper derives explicit power series expressions for conformal blocks involving operators with arbitrary spins in three-dimensional conformal field theories, expanding the toolkit for analyzing such theories.

Contribution

It provides new explicit formulas for conformal blocks with arbitrary spins in 3D CFTs using embedding space techniques, advancing the computational methods in the field.

Findings

Explicit power series expressions for conformal blocks with arbitrary spins.

Application of embedding space OPE results to derive conformal blocks.

Enhanced computational framework for 3D CFT analysis.

Abstract

We derive expressions for conformal blocks involving operators with arbitrary spins in 3-dimensional CFTs. We use previous results on the action of the OPE in the embedding space to derive the conformal blocks. The blocks are given as explicit power series in terms of the conformal cross ratios.