Lightcone expansions of conformal blocks in closed form

TL;DR

This paper derives new closed-form expressions for 4-point scalar conformal blocks in lightcone expansions, applicable to operators of any spin and in general dimensions, simplifying calculations in conformal field theory.

Contribution

It introduces explicit closed-form formulas for conformal blocks with arbitrary spin in lightcone expansions, advancing analytical tools in conformal field theory.

Findings

Formulas involve at most (ell+1) hypergeometric functions for spin ell.

Applicable to general dimensions and intermediate operator spins.

Simplifies the computation of conformal blocks in theoretical physics.

Abstract

We present new closed-form expressions for 4-point scalar conformal blocks in the s- and t-channel lightcone expansions. Our formulae apply to intermediate operators of arbitrary spin in general dimensions. For physical spin $\ell$, they are composed of at most $(\ell+1)$ Gaussian hypergeometric functions at each order.