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  • Open Access

Hodge duals in spherical compactifications

Arash Azizi*

  • The Institute for Quantum Science and Engineering, Texas A&M University, College Station, Texas 77843, USA

  • *Contact author: sazizi@tamu.edu
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Phys. Rev. D 112, 026026 – Published 24 July, 2025

DOI: https://doi.org/10.1103/57hd-7jrb

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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Phys. Rev. D 112, 026026– Published 24 July, 2025
  • Received 2 May 2025
  • Accepted 24 June 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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