An Explicit Kaluza-Klein Reduction of Einstein's Gravity in $6D$ on $S^2$
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| author | Dereli, Tekin Senikoglu, Yorgo |
| author_facet | Dereli, Tekin Senikoglu, Yorgo |
| contents | We study a six-dimensional Kaluza-Klein theory with spacetime topology $M_4 \times S^2$ and analyze the gauge sector arising from dimensional reduction. Using normalized Killing vectors on $S^2$, we explicitly construct the reduced Yang-Mills action and determine the corresponding gauge kinetic matrix. Despite the $SO(3)$ isometry of $S^2$, we show that only two physical gauge fields propagate in four dimensions. The gauge kinetic matrix therefore has rank two and possesses a single zero eigenvalue. We demonstrate that this degeneracy is a direct consequence of the coset structure $S^2 \simeq SO(3)/SO(2)$ and reflects a non-dynamical gauge direction rather than an inconsistency of the reduction. Our results clarify the geometric origin of gauge degrees of freedom in Kaluza-Klein reductions on coset spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_08443 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An Explicit Kaluza-Klein Reduction of Einstein's Gravity in $6D$ on $S^2$ Dereli, Tekin Senikoglu, Yorgo General Relativity and Quantum Cosmology High Energy Physics - Theory We study a six-dimensional Kaluza-Klein theory with spacetime topology $M_4 \times S^2$ and analyze the gauge sector arising from dimensional reduction. Using normalized Killing vectors on $S^2$, we explicitly construct the reduced Yang-Mills action and determine the corresponding gauge kinetic matrix. Despite the $SO(3)$ isometry of $S^2$, we show that only two physical gauge fields propagate in four dimensions. The gauge kinetic matrix therefore has rank two and possesses a single zero eigenvalue. We demonstrate that this degeneracy is a direct consequence of the coset structure $S^2 \simeq SO(3)/SO(2)$ and reflects a non-dynamical gauge direction rather than an inconsistency of the reduction. Our results clarify the geometric origin of gauge degrees of freedom in Kaluza-Klein reductions on coset spaces. |
| title | An Explicit Kaluza-Klein Reduction of Einstein's Gravity in $6D$ on $S^2$ |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2601.08443 |