Hexagonalization of Correlation Functions II: Two-Particle Contributions

TL;DR

This paper advances the computation of one-loop five-point functions in N=4 super-Yang-Mills theory using integrability, focusing on two-particle mirror contributions and confirming results with perturbation theory.

Contribution

It introduces techniques to evaluate two-particle mirror contributions in hexagon form factor approach for five-point functions, extending previous four-point analyses.

Findings

Agreement with perturbative results across analyzed cases

Two-particle contributions sum to zero for protected four-point functions

Tools developed facilitate higher-particle and higher-loop computations

Abstract

In this work, we compute one-loop planar five-point functions in $\mathcal{N}$=4 super-Yang-Mills using integrability. As in the previous work, we decompose the correlation functions into hexagon form factors and glue them using the weight factors which depend on the cross ratios. The main new ingredient in the computation, as compared to the four-point functions studied in the previous paper, is the two-particle mirror contribution. We develop techniques to evaluate it and find agreement with the perturbative results in all the cases we analyzed. In addition, we consider next-to-extremal four-point functions, which are known to be protected, and show that the sum of one-particle and two-particle contributions at one loop adds up to zero as expected. The tools developed in this work would be useful for computing higher-particle contributions which would be relevant for more complicated quantities such as higher-loop corrections and non-planar correlators.