Two-loop MHV Form Factors from the Periodic Wilson Loop

TL;DR

This paper develops a method to compute two-loop MHV form factors in planar $ ext{N}=4$ super Yang-Mills theory using periodic Wilson loops, addressing non-planar diagram contributions and divergence cancellations.

Contribution

It introduces a novel approach to calculate two-loop MHV form factors via periodic Wilson loops, including non-planar diagram effects and explicit two-loop examples.

Findings

Derived the integrand for two-loop n-particle MHV form factors.

Proved divergence cancellations at two loops.

Computed explicit 5- and 6-particle form factors.

Abstract

We discuss how to compute maximal-helicity-violating (MHV) form factors for the chiral part of the stress-tensor supermultiplet from periodic light-like polygon Wilson loops in planar $\mathcal N=4$ super Yang-Mills theory beyond the one-loop level. We show that the periodicity imposes path ordering on points on different edges, which explains the appearance of square roots coming from non-planar Feynman diagrams. Taking such diagrams into account, we provide the integrand of the two-loop $n$-particle MHV form factor, compute all diagrams, prove the cancellation of divergences and finally compute the two-loop 5-particle and 6-particle form factors as examples.