Analysis reveals Kaluza-Klein modes and mass spectrum of gauge fields in a six-dimensional model, indicating potential for novel symmetry breaking mechanisms.
We consider symmetry breaking of arbitrary gauge groups on a six-dimensional space-time which consists of a four-dimensional Minkowski space-time M⁴ and a two-dimensional sphere S². We expand the gauge fields in the presence of a non-trivial background unique to S². We analyze Kaluza-Klein(KK) modes of the gauge fields and derive the mass spectrum of the KK modes. We found that the gauge fields (not) commuting with the background fields (do not) remain symmetry operators in four dimensions. We also discuss the mass spectrum of the extra-dimensional components of the gauge fields and identify a physical scalar φ and a Nambu-Goldstone mode χ. As a result, we obtain a method to break gauge symmetry due to the nontrivial solution for gauge fields which is a unique feature of S².
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Asai et al. (2025) studied this question.
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