TOPOLOGICAL FORMULATION OF EFFECTIVE VORTEX STRINGS

We present a ''topological'' formulation of arbitrarily shaped vortex strings in four dimensional field theory. By using a large Higgs mass expansion, we then evaluate the effective action of the closed Abrikos ov-Nielsen-Olesen vortex string. It is shown that the effective action contains the Nambu-Goto term and an extrinsic curvature squared term with negative sign. We next evaluate the topological F-mu nu($) over t ilde F-mu nu term in the case where the vortex string manifold extends out to the boundary of the time direction of space-time and find that it becomes the sum of an ordinary self-intersection number and Polyak ov's self-intersection number of the world sheet swept by the vortex s tring. These self-intersection numbers are related to the self-linking number and the total twist number, respectively. Furthermore, the F-m u nu($) over tilde F-mu nu term turns out to be the difference between the sum of the writhing numbers and the linking numbers of the vortex strings at the initial time and the one at the final time. When the v ortex string is coupled to fermions, the chiral fermion number of the vortex string becomes the writhing number (module Z) through the chira l anomaly. Our formulation is also applied to ''global'' vortex string s in a model with a broken global U(1) symmetry.