Sphaleron decay on circles

Abstract

We discuss various sphaleron-like solutions on ${\mathbb{S}}^1$. These solutions are static, but unstable. We explore possible stabilization mechanisms based on the excitation of internal modes. Additionally, we observe that, on time scales comparable to the size of the circle, the collapse of large sphalerons mimics the kink-antikink scattering on the real line.

24 pages, 10 figures