Higher-dimensional applicability of cancellation methods

Determine whether the surface-exploration and cancellation techniques developed for two-dimensional large-N lattice Yang–Mills can be extended to higher dimensions.

Background

The explicit computations in the paper rely substantially on planarity and on the strong cancellations available in two dimensions. The authors note that in dimension three even a single plaquette has infinitely many plaquette assignments with non-zero surface sums, making cancellations substantially more intricate.

The unresolved problem is whether any of the exploration procedures and cancellation ideas can survive this higher-dimensional complexity, where shrinking loops and controlling contributing surfaces are more difficult.

References

The explicit computations performed throughout this paper heavily rely on the fact that we are in two dimensions. That being said, can any of the ideas or techniques developed in this paper be applied to higher dimensions?

— Surface sums in two-dimensional large-$N$ lattice Yang--Mills: Cancellations and explicit computation for general loops  (2508.13827 - Borga et al., 19 Aug 2025) in Section 1, Subsection “Triviality of the scaling limit and future research directions,” item 4