Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-06-30
Nucl.Phys.B436:100-128,1995
Physics
High Energy Physics
High Energy Physics - Theory
31page, LaTeX, 8 uuencoded epsf figures, KUNS-1269
Scientific paper
10.1016/0550-3213(94)00531-I
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 Abrikosov-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 $\FtF$ term and find that it becomes the sum of an ordinary self-intersection number and Polyakov's self-intersection number of the world sheet swept by the vortex string. These self-intersection numbers are related to the self-linking number and the total twist number, respectively. Furthermore, the $\FtF$ 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 vortex string is coupled to fermions, the chiral fermion number of the vortex string becomes the writhing number (modulo $\bZ$) through the chiral anomaly. Our formulation is also applied to ``global'' vortex strings in a model with a broken global $U(1)$ symmetry.
Sato* Masatoshi
Yahikozawa Shigeaki
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