Kaluza-Klein monopole with scalar multiplet hair

TL;DR

This paper constructs new Kaluza-Klein monopole solutions with scalar hair from a massive scalar multiplet, extending previous work and showing that higher multiplets lead to solutions with larger mass and angular momentum ranges.

Contribution

It introduces a method to generate scalar-haired Kaluza-Klein monopoles with arbitrary multiplet components, generalizing earlier doublet solutions and analyzing their properties.

Findings

Higher multiplets yield solutions with larger mass ranges.

Numerical solutions are provided for triplet and quadruplet cases.

The scalar hair modifies the monopole properties significantly.

Abstract

We construct Kaluza-Klein monopole solutions with scalar hair provied 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 generaize the preceding study on a doublet \cite{Brihaye:2023vox}. We find that the range of the mass and angular momentum of the hairy solutions are larger for higher multiplets.