Universal dualities for Wilson loops in lattice Yang-Mills

TL;DR

This paper uncovers a universal finite-N structure in Wilson loop expectations in lattice Yang-Mills theory, applicable across dimensions and gauge groups, revealing new insights through multiple analytical approaches.

Contribution

It introduces a universal, action-independent framework for Wilson loops in lattice Yang-Mills, connecting gauge, string, and spin-foam perspectives.

Findings

Factorization of terms into spectral weights and topological coefficients

Recovery of recent Wilson-action results as special cases

Development of a universal finite-N master loop equation

Abstract

We identify a universal finite-$N$ structure underlying Wilson loop expectations in lattice Yang-Mills, in any dimension $d\geq 2$, for gauge group $\mathrm{U}(N)$, and for arbitrary smooth central plaquette actions. The starting point is a state-sum expansion in plaquette labels by irreducible representations, in which each term factorizes into an action-dependent spectral weight and an action-independent topological coefficient. We then analyze these coefficients in three exact ways: as a gauge/string expansion over decorated spanning surfaces, as a local spin-foam/channel model on the dual incidence graph, and as a universal finite-$N$ master loop equation that closes on the coefficient side. As a consequence, several recent Wilson-action results are recovered as specializations of our broader action-agnostic framework.