Topological Influence between Monopoles and Vortices: a Possible Resolution of the Monopole Problem

Grand unified theories of fundamental forces predict that magnetic monopoles are inevitable in the Universe because the second homotopy group of the order parameter manifold is $\mathbb{Z}$. We point out that monopoles can annihilate in pairs due to an influence of Alice strings. As a consequence, a monopole charge is charactarized by ${\mathbb{Z}}_2$ rather than $\mathbb{Z}$ if the Universe can accommodate Alice strings, which is the case of certain grand unified theories.