Positive-geometric interpretation of multiple Wilson-loop BCFW recursion

Determine whether the BCFW-like recursion relations for correlators of multiple light-like Wilson loop operators define a description in terms of positive geometries, or a suitable generalization of positive geometries, analogous to the amplituhedron interpretation of ordinary BCFW recursion.

Background

The paper derives BCFW-like recursion relations for correlators of multiple light-like Wilson loops in N=4\mathcal{N}=4 super Yang–Mills theory. These relations generalize the recursion for a single Wilson loop and include terms involving self-intersections, loop correlators, and forward-limit contributions.

Ordinary BCFW recursion has a geometric interpretation as a triangulation of the amplituhedron. The authors explicitly raise the unresolved question of whether the multiple-loop recursion has an analogous interpretation through positive geometries or a broader geometric framework.

References

One pressing line of enquiry is whether the recursion relations which we have presented here hint at a description of Wilson loop correlators in terms of positive geometries (or some generalisation thereof). Since the ordinary BCFW recursion relations provide a triangulation of the amplituhedron, a natural question is whether these BCFW-like relations can play a similar role for a generalisation of the amplituhedron to the case of multiple loop operators.

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