Monopoles and fractional vortices in chiral superconductors

I discuss two exotic: objects that must be experimentally identified in chi ral superfluids and superconductors. These are (I? the vortex with a fracti onal quantum number (N = 1/2 in chiral superfluids, and N = 1/2 and N = 1/4 in chiral superconductors), which plays the part of the Alice string in re lativistic theories and (ii) the hedgehog in the <^>I field, which is the c ounterpart: of the Dirac magnetic monopole. These objects of different dime nsions are topologically connected. They form the combined object that is c alled a nexus in relativistic theories. In chiral superconductors, the nexu s has magnetic: charge emanating radially from the hedgehog, whereas the ha lf-quantum vortices play the part of the Dirac string, Each half-quantum vo rtex supplies the fractional magnetic flux to the hedgehog, representing 1/ 4 of the "conventional" Dirac string. I discuss the topological interaction of the superconductor's nexus with the 't Hooft-Polyakov magnetic monopole , which can exist in Grand Unified Theories. The monopole and the hedgehog with the same magnetic charge are topologically confined by a piece of the Abrikosov vortex. Such confinement makes the nexus a natural trap for the m agnetic monopole. Other properties of half-quantum vortices and monopoles a re discussed as well, including fermion zero modes.