Higher-Point Conformal Blocks in the Comb Channel

TL;DR

This paper presents a general method for computing higher-point conformal blocks in the comb channel for any number of points and dimensions, expanding the toolkit for conformal field theory analyses.

Contribution

It introduces a recursive approach to compute M-point conformal blocks in the comb channel for any dimension, filling a gap in the existing literature.

Findings

Validated results against known 5-point cases

Derived explicit formulas for arbitrary M and d

Confirmed consistency with existing literature

Abstract

We compute $M$-point conformal blocks with scalar external and exchange operators in the so-called comb configuration for any $M$ in any dimension $d$. Our computation involves repeated use of the operator product expansion to increase the number of external fields. We check our results in several limits and compare with the expressions available in the literature when $M=5$ for any $d$, and also when $M$ is arbitrary while $d=1$.