Finite-N manifestations of large-N surface-sum cancellations

Determine whether the concentration of surface-sum contributions identified in the large-N limit is already visible in finite-N surface sums for large N in the regime $\beta=\upbeta N$, and whether the large-N description can clarify the finite-N theory.

Background

A principal result of the paper shows that, in two dimensions at N=∞, all but a finite canonical collection of plaquette assignments cancel from the surface sum. The finite-N surface sums remain more complicated, and understanding their structure is relevant to extending existing finite-N results.

The authors ask whether the large-N cancellation phenomenon persists approximately for large but finite N, and whether the exact large-N description can provide useful information for the finite-N model and enlarge the parameter regime of known results.

References

Can this phenomenon already be observed in the finite-$N$ surface sum for large values of $N$ in the regime $\beta=\upbeta N$? More generally, could the complete description of the large-$N$ limit detailed in this paper inform our understanding of the finite-$N$ case in any meaningful way?

— 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 5