Dark Monopoles in Grand Unified Theories

TL;DR

This paper introduces a new class of monopole solutions called Dark Monopoles in certain Grand Unified Theories, which have unique magnetic properties and do not require a separate dark sector.

Contribution

It presents the theoretical construction of Dark Monopoles in Yang-Mills-Higgs theories with specific gauge symmetry breaking, including explicit solutions and their properties in the context of SU(5) GUT.

Findings

Dark Monopoles have magnetic fields orthogonal to the electromagnetic direction.

Their mass depends on the symmetry breaking scale and a function of coupling constants.

Dark Monopoles can exist without introducing a separate dark sector in GUTs.

Abstract

We consider a Yang-Mills-Higgs theory with gauge group $G=SU(n)$ broken to $G_{v} = [SU(p)\times SU(n-p)\times U(1)]/Z$ by a Higgs field in the adjoint representation. We obtain monopole solutions whose magnetic field is not in the Cartan Subalgebra. Since their magnetic field vanishes in the direction of the generator of the electromagnetic group $U(1)_{em}$, we call them Dark Monopoles. These Dark Monopoles must exist in some Grand Unified Theories (GUTs) without the need to introduce a dark sector. We analyze the particular case of $SU(5)$ GUT, where we obtain that their mass is $M = 4\pi v \widetilde{E}(\lambda/e^{2})/e$, where $\widetilde{E}(\lambda/e^{2})$ is a monotonically increasing function of $\lambda/e^{2}$ with $\widetilde{E}(0)=1.294$ and $\widetilde{E}(\infty)=3.262.$ We also give a geometrical interpretation to their non-abelian magnetic charge.