Cluster compatibility of poles in Wilson-loop correlator recursion

Determine whether the BCFW representations for correlators of multiple light-like Wilson loop operators possess a notion of cluster compatibility for the poles common to each term, analogous to cluster compatibility for a single Wilson loop.

Background

The BCFW representation for a single Wilson loop has been studied in relation to cluster-algebra structures, including compatibility among poles appearing in different terms. The recursion relations developed in the paper produce representations for correlators involving multiple Wilson loops, whose pole structure may be more complicated.

The authors explicitly leave unresolved whether an analogous cluster-compatibility property exists for the common poles of the terms in the multiple-loop correlator representation.