Gaussian limits of lattice Higgs models with complete symmetry breaking

TL;DR

This paper establishes a Gaussian scaling limit for lattice Yang-Mills-Higgs models with any compact Lie group, showing how the theory simplifies to a Gaussian form under certain scaling conditions, extending previous results for SU(2).

Contribution

It generalizes the Gaussian limit result to arbitrary compact connected Lie groups in the complete symmetry breaking regime, broadening the understanding of lattice gauge theories.

Findings

Gaussian limit established for all compact connected Lie groups

The limit occurs as lattice spacing goes to zero and coupling constant increases

Extends previous SU(2) results to general Lie groups

Abstract

Given any compact connected matrix Lie group $G$ and any lattice dimension $d\ge 2$, we construct a massive Gaussian scaling limit for the $G$-valued lattice Yang-Mills-Higgs theory in the "complete breakdown of symmetry" regime. This limit arises as the lattice spacing tends to zero and the (inverse) gauge coupling constant tends to infinity sufficiently fast, causing the theory to "abelianize" and yield a Gaussian limit. This complements a recent work by Chatterjee (arXiv:2401.10507), which obtained a similar scaling limit in the special case $G= SU(2)$.