Half-Integer Winding Number Solutions to the Landau-Ginzburg-Higgs Equations and Instability of the Abrikosov-Nielsen-Olesen Vortex

New solutions to the abelian U(1) Higgs model, corresponding to vortices of integer and half-integer winding number bound onto the edges of domain walls and possibly surrounded by annular current flows, are described, based on a fine-grained analysis of the topology of such configurations in spacetime. The existence of these states, which saturate BPS bounds in specific limits and are quite reminiscent of D-branes and membranes in general, could have interesting and some important consequences in a wide range of physical contexts. For instance, they raise the possibility that for some regimes of couplings the usual vortex of unit winding number would split into two vortices each of one-half winding number bound by a domain wall. A similar approach may also be relevant to other known topological states of field theory.