Dark monopoles in Grand Unified Theories

Abstract

We consider a Yang-Mills-Higgs theory with gauge group G = SU(n) broken to Gv = [SU(p) × SU(n − p) × 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 U(1)em electromagnetic group, 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 = 4πvẼ(λ/e2)/e, where Ẽ(λ/e2) is a monotonically increasing function of λ/e2 with Ẽ(0) = 1.294 and Ẽ(∞) = 3.262. We also give a geometrical interpretation to their non-abelian magnetic charge.