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arXiv · 2507.06324

Hodge Duals in Spherical Compactifications

Arash Azizi
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Abstract

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.

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Arash Azizi. 2025-07-08. Hodge Duals in Spherical Compactifications. https://arxiv.org/abs/2507.06324

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