Hodge Duals in Spherical Compactifications
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911046558547968 |
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| author | Azizi, Arash |
| author_facet | Azizi, Arash |
| contents | We present a general formalism for computing the Hodge dual of differential forms in arbitrary dimensions subject to a spherical constraint. This problem arises naturally in Kaluza-Klein compactifications, where sphere reductions demand careful treatment of differential forms constrained to lie on embedded submanifolds. We derive an explicit expression for the Hodge dual of a $p$-form in the presence of such constraints and validate our general ansatz through illustrative examples in three dimensions, including both flat and diagonal metric backgrounds. The resulting framework offers a systematic and practical tool for handling constrained Hodge duals, with direct applications to consistent truncations in supergravity and string theory compactifications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06324 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hodge Duals in Spherical Compactifications Azizi, Arash High Energy Physics - Theory We present a general formalism for computing the Hodge dual of differential forms in arbitrary dimensions subject to a spherical constraint. This problem arises naturally in Kaluza-Klein compactifications, where sphere reductions demand careful treatment of differential forms constrained to lie on embedded submanifolds. We derive an explicit expression for the Hodge dual of a $p$-form in the presence of such constraints and validate our general ansatz through illustrative examples in three dimensions, including both flat and diagonal metric backgrounds. The resulting framework offers a systematic and practical tool for handling constrained Hodge duals, with direct applications to consistent truncations in supergravity and string theory compactifications. |
| title | Hodge Duals in Spherical Compactifications |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2507.06324 |