On collinear factorization of Wilson loops and MHV amplitudes in N=4 SYM

TL;DR

This paper investigates the collinear factorization of Wilson loops and MHV amplitudes in N=4 SYM, analyzing strong and weak coupling regimes, and provides proofs and estimates for splitting functions and Ward identities.

Contribution

It offers a detailed analysis of collinear factorization in N=4 SYM, including proofs of Ward identities and methods to compute splitting functions at different coupling strengths.

Findings

Computed splitting functions in specific cases.

Proved the anomalous Ward identity at strong coupling.

Suggested strategies for higher-order perturbative proofs.

Abstract

We consider the (multi) Splitting function of Wilson loops and MHV gluon scattering S matrix elements in N=4 SYM. At strong coupling, one can utilize the methods of Alday and Maldacena and at weak coupling (one loop) the correspondence to light like Wilson loops is used. In both cases, the (multi) Splitting function corresponds to flattened cusps in the light like polygon, allowing for a clean disentanglement from the other gluons. We compute it in some cases and estimate some terms in other cases. We also prove the anomalous Ward identity of Drummond et al. in the strong coupling regime. Lastly, we briefly comment on a possible strategy for a proof of collinear factorization of Wilson loops at higher orders of perturbation theory.