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Kaluza-Klein monopole with scalar multiplet hair

Takaaki Ishii1,*, Keiju Murata2,†, and Keita Sugawara2,‡

  • 1Department of Physics, College of Science, Rikkyo University, Nishi-Ikebukuro, Tokyo 171-8501, Japan
  • 2Department of Physics, College of Humanities and Sciences, Nihon University, Sakurajosui, Tokyo 156-8550, Japan

  • *Contact author: ishiitk@rikkyo.ac.jp
  • †Contact author: murata.keiju@nihon-u.ac.jp
  • ‡Contact author: chkt23002@g.nihon-u.ac.jp
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Phys. Rev. D 112, 104062 – Published 21 November, 2025

DOI: https://doi.org/10.1103/znjv-vszl

Abstract

We construct Kaluza-Klein monopole solutions with scalar hair provided by a massive complex scalar field multiplet that minimally couples to five-dimensional Einstein gravity. Writing the scalar field multiplet in terms of the Wigner D-matrices, we introduce the ansatz of the scalar multiplet compatible with the symmetries of the Gross-Perry-Sorkin monopole, on which the scalar hair grows. We give the ansatz for a multiplet with arbitrary number of components, whereas we show numerical solutions of the hairy Kaluza-Klein monopole specifically for the cases of scalar triplet and quadruplet. These generalize the preceding study on a doublet [J. High Energy Phys. 01 (2024) 181]. We find that the range of the mass and angular momentum of the hairy solutions are larger for higher multiplets.

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Phys. Rev. D 112, 104062– Published 21 November, 2025
  • Received 15 September 2025
  • Accepted 5 November 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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