Non-trivial high-temperature-regime Wilson loop limits

Determine whether new limiting Wilson loop expectations for inverse temperature values greater than one admit a rescaling in the lattice mesh that yields non-trivial continuum limits.

Background

The surface-sum representation established in the companion work cannot hold for inverse-temperature parameter values greater than one. The paper therefore anticipates that a different family of limiting Wilson loop expectations, denoted by φ′(ℓ), would be needed in that regime.

The open question is whether such alternative limiting expectations could have formulas compatible with a lattice-mesh rescaling that produces a non-trivial continuum limit, unlike the trivial limit obtained from the formulas analyzed in the paper.

References

Is it possible that such new limiting Wilson loop expectations $\phi'(\ell)$ yields new formulas that admit a rescaling of $\upbeta$ in $\delta$ leading to non-trivial limits?

— 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 2