I discuss two exotic objects that must be experimentally identified in chiral superfluids and superconductors. These are (I) the vortex with a fractional quantum number (N = 1/2 in chiral superfluids, and N = 1 /Z and N = 1 /4 in chiral superconductors). which plays the part of the Alice String in relativistic theories and (ii) the hedgehog in the I field, which is the counterpart of the Dirac magnetic monopole. These objects of different dimensions are topologically connected. They form the combined object that is called a nexus in relativistic theories. In chiral superconductors, the nexus has magnotic charge emanating radially from the hedgehog, whereas the half-quantum vortices play the part of the Dirac string. Each half-quantum vortex supplies the fractional magnetic flux to the hedgehog, representing 1/4 of the "conventional" Dirac string. l discuss the topological interaction of the superconductor's nexus with the 't Hooffpolyakov magnetic mono- pole, 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 magnetic monopole. Other properties of half-quantum vortices and monopoles are discussed as well. including fermion zero modes.
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