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PreprintCC BY 4.0arXiv

A variational approach for the 2D Abelian Yang-Mills-Higgs measure

  • Nikolay Barashkov
  • Ajay Chandra
  • Ilya Chevyrev
  • Andreas Koller
  • Abdulwahab Mohamed
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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.

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Cite

BibTeXRIS
BibTeX
@misc{barashkov2026variational,
  title = {{A variational approach for the 2D Abelian Yang-Mills-Higgs measure}},
  author = {Nikolay Barashkov and Ajay Chandra and Ilya Chevyrev and Andreas Koller and Abdulwahab Mohamed},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.21972},
  eprint = {2609.21972},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.21972},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A variational approach for the 2D Abelian Yang-Mills-Higgs measure
AU  - Nikolay Barashkov
AU  - Ajay Chandra
AU  - Ilya Chevyrev
AU  - Andreas Koller
AU  - Abdulwahab Mohamed
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2609.21972
UR  - https://arxiv.org/abs/2609.21972
AB  - 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.
ER  -