Multichannel conformal blocks for scattering amplitudes

TL;DR

This paper develops multichannel conformal blocks for scattering amplitudes in planar N=4 super Yang-Mills theory by resumming fermion-antifermion pairs, leading to a new flux-tube partial wave framework expressed through Lauricella-Saran hypergeometric series.

Contribution

It introduces a novel construction of multichannel conformal blocks using resummation techniques within the flux-tube picture, connecting to the OPE framework and hypergeometric series.

Findings

Construction of multichannel conformal blocks for NMHV polygons

Expression of conformal partial waves via Lauricella-Saran hypergeometric series

Establishment of a link between flux-tube resummation and conformal partial waves

Abstract

By performing resummation of small fermion-antifermion pairs within the pentagon form factor program to scattering amplitudes in planar N = 4 superYang-Mills theory, we construct multichannel conformal blocks within the flux-tube picture for N-sided NMHV polygons. This procedure is equivalent to summation of descendants of conformal primaries in the OPE framework. The resulting conformal partial waves are determined by multivariable hypergeometric series of Lauricella-Saran type.