VII OFICINA NACIONAL DE TEORIA QUÂNTICA DE CAMPOS //////////////////// VII NATIONAL WORKSHOP ON QUANTUM FIELD THEORY

Dark Monopoles in Grand Unified Theories

10 Dec 2021, 15:15

10m

Virtual Meeting, Universidade Federal da Bahia, Brazil

Vídeo-Poster Apresentações de vídeo-pôsteres

Speaker

Ms Maria de Lourdes Deglmann

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 $\varphi$ 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 $r\to 0$ and $r\to \mathrm{\infty }$. 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 $\tilde{E}(\mathrm{\infty })=3.262$. 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 $J_M^{\mu }$, 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.

Presentation materials

Link do vídeo: https://youtu.be/HoozLrsCExA