Multi-phases in gauge theories on non-simply connected spaces

TL;DR

This paper explores the complex phase structures of SU(2) gauge theories on non-simply connected spaces, revealing multiple phases and phase transitions that could impact grand unified theories and the gauge hierarchy problem.

Contribution

It demonstrates the existence of multiple phases in gauge theories on non-simply connected spaces and explicitly determines critical radii and transition orders.

Findings

Identifies three phases: Hosotani, Higgs, and coexisting.

Determines critical radius and phase transition order.

Suggests implications for GUT scenarios and gauge hierarchy problem.

Abstract

It is pointed out that phase structures of gauge theories compactified on non-simply connected spaces are not trivial. As a demonstration, an SU(2) gauge model on $M^3\otimes S^1$ is studied and is shown to possess three phases: Hosotani, Higgs and coexisting phases. The critical radius and the order of the phase transitions are explicitly determined. A general discussion about phase structures for small and large scales of compactified spaces is given. The appearance of phase transitions suggests a GUT scenario in which the gauge hierarchy problem is replaced by a dynamical problem of how to stabilize a radius of a compactified space in close vicinity to a critical radius.