Gauge Vortices

The properties and interactions of gauge vortices are discussed in a variety of contexts. When quarks and leptons propagate in the background of a grand unified cosmic string, various baryon number violating processes can occur. We argue that, because of the pure gauge field that surrounds the string, the cross-sections for these processes are generically enhanced by large factors over the naive, geometric, cross section. This is the cosmic string analog of the Callan-Rubakov effect. We then investigate the bosonic zero modes of vortices formed in the gauge symmetry breaking G to H. For nonabelian G such zero modes are generic. Vortices render the embedding H subset \G^ace-dependent, with a dynamically determined subgroup ~ H single-valued; gauge bosons associated with multi -valued generators Aharonov-Bohm scatter off the vortex. Alice strings (H = O(2), ~ H = doubz _2) attract charges, scatter SO(2) "photons," and a loop possesses modes with unlocalizable "Cheshire" charge. Next we consider the physics of discrete gauge symmetries in the continuum. Details of the measurement of discrete charges by the Aharonov-Bohm scattering of vortices are discussed. We take the first steps toward the extension of such discrete gauge symmetries to the nonabelian case. We then consider vortices in (2 + 1) -dimensional abelian Higgs theories with an additional Chern -Simons term. These vortices behave as anyons, excitations possessing fractional statistics. The P and T violating vortex-vortex cross-section is calculated, and it is pointed out that P and T violating effects are the most characteristic signature of the "anyonic superconductors" that have been suggested as theoretical models of the new high-T _ c superconductors. Finally, the difficulties of communication between different branches of theoretical physics are briefly considered.