Non-planar generalization of planar one-loop leading singularities

Determine whether the familiar planar one-loop leading-singularity formulae for a single Wilson loop expectation value admit non-planar generalizations expressed in terms of correlators, rather than products, of Wilson loop operators at tree level.

Background

The paper establishes an explicit connection between colour-exact correlators of rr Wilson loops and correlators of r+1r+1 Wilson loops at lower MHV degree. In particular, non-planar corrections to a single Wilson loop are related to multiple-loop correlation functions.

This structure motivates the unresolved question of whether planar one-loop leading singularities can be extended beyond the planar limit. The proposed form would involve tree-level correlators of loop operators instead of products of individually evaluated loop operators.

References

It would be interesting to explore whether, as a consequence, the familiar formulae for the planar one-loop leading singularities of a single Wilson loop's expectation value admit non-planar generalisations, for instance in terms of correlators, rather than products, of loop operators at tree level.

— BCFW recursion for light-like Wilson loop correlators  (2608.19418 - Drummond et al., 19 Aug 2026) in Section Conclusions