Monopole core and mass scales in an SU(5) transition ($M_M\sim 4\pi \eta /g$)

For simply connected space $SU(5)$ broken to the connected Standard Model subgroup, the exact homotopy sequence gives ${\pi }_2(G/H)\cong {\pi }_1(H)\cong \mathbb{Z}$. Stable magnetic monopoles form. Their gauge and scalar cores have scales $(g\eta {)}^{-1}$ and $(\sqrt{\lambda }\eta {)}^{-1}$; their masses are $M_M\sim 4\pi \eta /g$ times a dimensionless profile factor. The physical subgroup is $(SU(3)\times SU(2)\times U(1))/{\mathbb{Z}}_6$, which retains an infinite-cyclic fundamental group.

// Target: cosmology.bigb