Year: 2026
Type: preprint
Abstract: We use the Boué-Dupuis variational method to construct the Abelian Yang-Mills-Higgs measure on the two-dimensional torus with polynomial Higgs potentials, giving, to our knowledge, the first rigorous construction of an interacting gauge theory by this approach. We first use the variational method to construct the Higgs field conditioned on the gauge field, with a covariant Gaussian free field as the reference measure. Integrating out the Higgs field produces a weight on the gauge field, which we control through a second application of the variational method. We also prove new exponential integrability estimates for the joint gauge-Higgs field and establish gauge covariance. Finally, we prove convergence of the Laplace transforms of the regularised measures and establish a new large-deviation principle for gauge-invariant observables in the semiclassical limit.
Source: arXiv (Cornell University)
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213926898