A probabilistic mechanism for quark confinement

TL;DR

This paper provides a rigorous mathematical proof linking unbroken center symmetry in lattice gauge theories to quark confinement, confirming a longstanding heuristic in physics.

Contribution

It rigorously defines center symmetry in lattice gauge theories and proves that unbroken center symmetry implies confinement, offering a new mathematical foundation for this physical phenomenon.

Findings

Unbroken center symmetry implies quark confinement.

A nontrivial gauge group center with exponential decay of correlations ensures unbroken symmetry.

The paper confirms the heuristic that confinement results from unbroken center symmetry.

Abstract

The confinement of quarks is one of the enduring mysteries of modern physics. There is a longstanding physics heuristic that confinement is a consequence of `unbroken center symmetry'. This article gives mathematical confirmation of this heuristic, by rigorously defining of center symmetry in lattice gauge theories and proving that a theory is confining when center symmetry is unbroken. Furthermore, a sufficient condition for unbroken center symmetry is given: It is shown that if the center of the gauge group is nontrivial, and correlations decay exponentially under arbitrary boundary conditions, then center symmetry does not break.