Existence and Stability of Semilocal Cosmic Strings

The Semilocal Strings are Metastable Vortex Configurations which appear in theories where the vacuum manifold may not have non-trivial topological properties. Their metastabity is realized for a finite sector of parameter space. It   is due to the effects of gauge fields whose symmetry group is selected to affect only a subspace of  the vacuum manifold. This subspace (if isolated) would have non-trivial topological properties.

The simplest model that incorporates semilocal strings was first studied by Vachaspati and Achucarro (Phys.Rev.D44:3067-3071,1991). The stability of the semilocal vortices was first studied analyticaly by Hindmarsh (Phys.Rev.Lett.68:1263-1266,1992) and using numerical simulations by Achucarro, Kuijken, Perivolaropoulos and Vachaspati (Nucl.Phys.B388:435-456,1992).   The most interesting physical application of Semilocal Strings is their Embedding in the Standard Electroweak Model which was first done by Vachaspati (Nucl.Phys.B397:648-671,1993). The Stability of these Electroweak Strings was first studied by James, Perivolaropoulos and Vachaspati (Phys.Rev.D46:5232-5235,1992) who found that there is a finite sector in the parameter space of the electroweak model where these strings are metastable. This sector however does not include the experimentally measured values of the Standard Model Parameters. This was the first time  that metastable soliton solutions were found in the Standard Electroweak Model. A conceptual generalization of semilocal strings was recently done by Axenides, Perivolaropoulos and Tomaras (Phys.Rev.D58:103512,1998).

The simplest model that incorporates semilocal strings has a single free parameter called beta (β). For beta > 1 the semilocal strings were shown to be unstable towards decay to the trivial vacuum configuration while for beta < 1 they are metastable.

The following links lead to plots corresponding to frames of the simulation of the evolution of an isolated semilocal string at T=0, T=60 and T=100 (wth timestep size dt=0.2) for beta=1.1 and beta=0.9.  More details can be found in Nucl.Phys.B388:435-456,1992.

Parameter beta = 1.1 (β=1.1): The frames indicate the distribution of the energy density in 2d space at evolution times: T=0, T=60, T=100 which correspond to timesteps N=0, N=300, N=500. The instability of the initial configuration is demonstrated.

Parameter beta = 0.9 (β=0.9): The frames indicate the distribution of the energy density in 2d space at evolution times: T=0, T=60, T=100 which correspond to timesteps N=0, N=300, N=500. The stability of the initial configuration is demonstrated.

Click here to dowload the full Origin 5.0 file with graphs and data. You may also download a single zipped ps-file showing the evolution of a stable or unstable semilocal string including the three frames of evolution.