By Ruark A.E.

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As with any new algorithm, it is essential to check that it reproduces previously known results accurately, and this has been done in [3]. Note that setting "0 in the semilocal model obtains the Abelian Higgs model, thus comparison with topological strings is straightforward, and it is used repeatedly as a test case, both to check the simulation techniques and to minimise systematic errors when quoting formation rates. erent ways: (a) restriction to the Abelian Higgs model gives good agreement with analytic and numerical estimates for cosmic strings in [130]; (b) the results are robust under varying initial conditions and numerical viscosities (see Fig.

183) J S C B In other words, and u travel parallel to the string #ux while e and d travel anti-parallel to the * string #ux. We should mention that the picture of quarks travelling along the Z-string (see Fig. ects have been totally ignored. At the present time it is not known if the strong forces of QCD will con"ne the quarks on the string into mesons and baryons (for example, Fig. 13. The direction of propagation of quark and lepton zero modes on the Z-string. 402 A. Achu& carro, T. Vachaspati / Physics Reports 327 (2000) 347}426 pions and protons).

These have been solved in the background of a straight Z string in [40,50,99]. 3). A discussion of the fermion zero modes in connection with index theorems can be found in [82,79]. e\ P 0 0 eP 0 0 0 ! ie P 0 0 0 0 0 0 ie\ P 0 0 ie P 0 " 0 1 1 0 . 1 0 0 1 ( ), e " i ( ), 0 0 1 (170) A. Achu& carro, T. 1)v ! h f . (2 (171) (172) In these equations q is the eigenvalue of the operator q de"ned in Eq. (87) and denotes the Z-charge of the various left-handed fermions. ) The boundary conditions are that and should vanish asymptotically.