Homotopy transfer for massive Kaluza-Klein modes
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866910197128101888 |
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| author | Eloy, Camille Hohm, Olaf Lavino, Camilla Samtleben, Henning Simon, Yehudi |
| author_facet | Eloy, Camille Hohm, Olaf Lavino, Camilla Samtleben, Henning Simon, Yehudi |
| contents | We develop techniques to treat massive Kaluza-Klein modes to arbitrary order in perturbation theory. The Higgs mechanism that renders the higher Kaluza-Klein modes massive is displayed. To this end we give an algorithm in perturbation theory that yields new fields with the following characteristics: they are gauge invariant under all higher-mode gauge transformations, which are broken, but they transform covariantly under the zero-mode gauge transformations, which are unbroken. We employ the formulation of field theory in terms of $L_{\infty}$ algebras together with their homotopy transfer, which here maps the gauge redundant fields of gravity to gauge invariant fields. We illustrate these results, as a proof of concept, for Kaluza-Klein theory on a torus. In an accompanying paper these results will be applied to a large class of generalized Scherk-Schwarz backgrounds in exceptional field theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03146 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Homotopy transfer for massive Kaluza-Klein modes Eloy, Camille Hohm, Olaf Lavino, Camilla Samtleben, Henning Simon, Yehudi High Energy Physics - Theory We develop techniques to treat massive Kaluza-Klein modes to arbitrary order in perturbation theory. The Higgs mechanism that renders the higher Kaluza-Klein modes massive is displayed. To this end we give an algorithm in perturbation theory that yields new fields with the following characteristics: they are gauge invariant under all higher-mode gauge transformations, which are broken, but they transform covariantly under the zero-mode gauge transformations, which are unbroken. We employ the formulation of field theory in terms of $L_{\infty}$ algebras together with their homotopy transfer, which here maps the gauge redundant fields of gravity to gauge invariant fields. We illustrate these results, as a proof of concept, for Kaluza-Klein theory on a torus. In an accompanying paper these results will be applied to a large class of generalized Scherk-Schwarz backgrounds in exceptional field theory. |
| title | Homotopy transfer for massive Kaluza-Klein modes |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2512.03146 |