Leading singularities of Wilson loop correlators from twistor Wilson loop diagrams

TL;DR

This paper demonstrates that the factorisation of one-loop leading singularities in planar $ ext{N}=4$ super Yang-Mills theory can be directly observed in twistor Wilson loop diagrams, providing a new geometric perspective on dualities.

Contribution

It shows that the factorisation of one-loop leading singularities is manifest in twistor Wilson loop diagrams, offering a planarity-based derivation without unitarity arguments.

Findings

Factorisation is manifest at the level of twistor Wilson loop diagrams.

Derived compact formulae for leading singularities of multiple Wilson loop correlators.

Provided a simple method to compute $O(g^2)$ Wilson loop correlators at any MHV degree.

Abstract

The leading singularities of one-loop scattering amplitudes in planar $\mathcal{N}=4$ super Yang-Mills theory are known to factorise into products of tree-level amplitudes, and this can be seen from a number of different perspectives e.g. generalised unitarity or on-shell diagrams. Here we investigate the leading singularities from the perspective of the Wilson loop expectation values to which these amplitudes are dual, in particular making use of the twistor Wilson loop formalism. We show that the factorisation of one-loop leading singularities of a null Wilson loop's expectation value into a product of tree-level objects is manifest at the level of twistor Wilson loop diagrams, and is a simple consequence of planarity, without appeal to e.g. unitarity on the amplitude side of the duality. We then use the same approach to derive compact formulae for the one-loop leading singularities of correlators of multiple light-like Wilson loop operators in terms of tree-level objects. Via the chiral box expansion, these formulae provide a simple route to writing down the $O(g^2)$ correlation function of any number of Wilson loops at any MHV degree.