Resumming the POPE at One Loop

TL;DR

This paper demonstrates how to resum the Pentagon Operator Product Expansion series at one loop for hexagonal Wilson loops in planar N=4 super Yang-Mills, reproducing known results through effective excitation summation.

Contribution

It introduces a method to resum the POPE series at one loop level for hexagonal Wilson loops, providing explicit integral expressions.

Findings

Reproduces the known one-loop six-point MHV amplitude.

Expresses the resummed series in terms of logarithms and polylogarithms.

Validates the effectiveness of the resummation approach.

Abstract

The Pentagon Operator Product Expansion represents polygonal Wilson loops in planar $\mathcal{N}=4$ super Yang-Mills in terms of a series of flux tube excitations for finite coupling. We demonstrate how to re-sum this series at the one loop level for the hexagonal Wilson loop dual to the six-point MHV amplitude. By summing over a series of effective excitations we find expressions which integrate to logarithms and polylogarithms, reproducing the known one-loop result.