Symmetry Breaking/Restoration in a Non-Simply Connected Space-Time

TL;DR

This paper explores the complex phase structure of field theories on non-simply connected spaces, highlighting symmetry breaking/restoration at critical radii and the spontaneous breakdown of translational invariance, using the O(N) model as an example.

Contribution

It reveals a novel phase structure in field theories on non-simply connected spaces, including classical and quantum-induced symmetry transitions and translational invariance breaking.

Findings

Identification of critical radii for symmetry transitions

Demonstration of classical and quantum phase transitions

Observation of spontaneous translational invariance breaking

Abstract

Field theories compactified on non-simply connected spaces, which in general allow to impose twisted boundary conditions, are found to unexpectedly have a rich phase structure. One of characteristic features of such theories is the appearance of critical radii, at which some of symmetries are broken/restored. A phase transition can occur at the classical level, or can be caused by quantum effects. The spontaneous breakdown of the translational invariance of compactified spaces is another characteristic feature. As an illustrative example,the O(N) $\phi^4$ model on $M^3\otimes S^1$ is studied and the novel phase structure is revealed.