Deconfinement For $\mathrm{SO}(3)$ Lattice Yang-Mills at Strong Coupling

TL;DR

This paper rigorously proves that $ ext{SO}(3)$ lattice Yang-Mills theory at strong coupling does not meet Wilson's criterion for quark confinement, confirming a physics prediction for theories with trivial center groups.

Contribution

It provides a rigorous mathematical proof that $ ext{SO}(3)$ lattice Yang-Mills theory fails Wilson's confinement criterion at strong coupling, supporting prior physics predictions.

Findings

$ ext{SO}(3)$ lattice Yang-Mills does not satisfy Wilson's criterion at strong coupling

Confirms physics predictions about trivial center gauge groups and confinement

Provides a rigorous mathematical foundation for these results

Abstract

We make rigorous the physics prediction that lattice Yang-Mills theories with gauge groups which have trivial centers do not satisfy Wilson's criterion for quark confinement. Specifically we prove that $\mathrm{SO}(3)$ lattice Yang-Mills theory does not satisfy Wilson's criterion in a strong coupling regime.