Speaker
Description
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 $\phi$ in the adjoint representation. We obtain monopole solutions whose magnetic field does not lie in the Cartan Subalgebra. And, since their magnetic field vanishes in the direction 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 calculate the general hamiltonian and equations of motion, while we also obtain approximate analytical solutions when $r\to0$ and $r\to\infty$. We show that their mass is given by $M=\frac{4\pi v}{e}\,\tilde {E}(\lambda/e^{2})$, where $\tilde{E}(\lambda/e^{2})$ is a monotonically increasing function of $\lambda/e^{2}$, with the lower and upper bounds depending on specific parameters of each possible symmetry breaking. For the particular case of the $SU(5)$ GUT, we obtain that $\tilde{E}(0) = 1.294$ and $\tilde{E}(\infty)= 3.262$. In addition, we give a geometrical interpretation to their non-abelian magnetic charge and we show that our monopole solution has a conserved magnetic current $J^{\mu}_{M}$, which is quantized and lies in a non-abelian direction. Finally, we proceed with an asymptotic stability analysis of these $SU(n)$ Dark Monopole solutions, where we show that there are unstable modes associated with them. We obtain the explicit form of the unstable perturbations and the associated negative-squared eigenfrequencies.
