Lattice gauge theories are regularized versions of quantum field theories: space is discrete, fields live on edges, and the continuum limit recovers the physical theory. The Yang–Mills–Higgs theory on a lattice combines a gauge field (connection) with a Higgs field (symmetry-breaking scalar). In the regime of “complete symmetry breaking,” the Higgs field gives mass to all gauge bosons.
The paper on Gaussian limits of lattice Higgs models (arXiv: 2603.24555) proves that in this regime, for any compact connected matrix Lie group G and any dimension d ≥ 2, the scaling limit is a massive Gaussian field.
The mechanism is abelianization. When the inverse gauge coupling grows fast enough as the lattice spacing shrinks, the non-abelian structure of G becomes irrelevant — the theory reduces to its abelian part. The fluctuations around the broken-symmetry vacuum are Gaussian because the potential is quadratic to leading order, and the non-abelian corrections are suppressed.
The result is universal in G: it holds for any compact connected Lie group, not just SU(2) (which was the previously known case). The complete breaking of symmetry is what makes the theory massive, and massive theories are Gaussian at weak coupling.
The through-claim: complete symmetry breaking linearizes the theory. When every direction of symmetry is broken, every gauge boson acquires mass, the potential becomes effectively quadratic, and the continuum limit is free (Gaussian). The non-abelian structure — the source of all the richness in gauge theory — is suppressed when every symmetry is consumed by the Higgs mechanism.
2603.24555. Mathematical physics / lattice gauge theory / Higgs mechanism / scaling limits / Gaussian fields.