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. In a companion work, this framework is used to construct the higher-dimensional heat-kernel master field at strong coupling and to prove an area-law bound.
From: Thibaut Lemoine [view email]
[v1]
Fri, 17 Apr 2026 17:11:50 UTC (240 KB)
[v2]
Sun, 9 Aug 2026 20:06:03 UTC (235 KB)
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