Topological Classification of Symmetry Breaking and Vacuum Degeneracy
High Energy Physics - Theory
2026-03-05 v2 Mathematical Physics
Differential Geometry
math.MP
Abstract
We argue that a general system of scalar fields and gauge fields manifesting vacuum degeneracy induces a principal groupoid bundle over spacetime and that the pattern of spontaneous symmetry breaking and the Higgs mechanism are encoded by the singular foliation canonically induced on the moduli space of scalar vacuum expectation values by the Lie groupoid structure. Recent mathematical results in the classification of singular foliations then provide a qualitative classification of the possible patterns of vacuum degeneracy.
Keywords
Cite
@article{arxiv.2406.17634,
title = {Topological Classification of Symmetry Breaking and Vacuum Degeneracy},
author = {Simon-Raphael Fischer and Mehran Jalali Farahani and Hyungrok Kim and Christian Saemann},
journal= {arXiv preprint arXiv:2406.17634},
year = {2026}
}
Comments
13 pages, 5 figures, 1 table; v2: Some smaller adjustments, thanks to the referee