Semilocal and Electroweak Strings

Abstract

We review a class of non-topological defects in the standard electroweak model, and their implications. Starting with the semilocal string, which provides a counterexample to many well known properties of topological vortices, we discuss electroweak strings and their stability with and without external influences such as magnetic fields. Other known properties of electroweak strings and monopoles are described in some detail and their potential relevance to future particle accelerator experiments and to baryon number violating processes is considered. We also review recent progress on the cosmology of electroweak defects and the connection with superfluid helium, where some of the effects discussed here could possibly be tested.

Figures (22)

• Figure 1: The functions $f_{NO}$, $v_{NO}$ for a string with winding number $n=1$ (top panel) and $n=50$ (bottom panel), for $\beta \equiv 2\lambda/q^2 = 0.5$. The radial coordinate has been rescaled as in eq. (\ref{['natural']}), $\hat{\rho} = q\eta \rho/\sqrt{2}$.
• Figure 2: A two-dimensional simulation of the evolution of a perturbed isolated semilocal string with $\beta >1$, from AchKuiPerVac92. The plot shows the (rescaled) energy density per unit length in the plane perpendicular to the string. $\beta = 1.1$ The initial conditions include a large destabilizing perturbation in the core, $\Phi^T(t=0) = (1, f_{NO}(\rho) e^{i\varphi})$, which is seen to destroy the string.
• Figure 3: The evolution of a string with $\beta <1$. The initial configuration is the same as in Fig. \ref{['unstablestring']} but now, after a few oscillations, the configuration relaxes into a semilocal string, $\Phi^T = (0, f_{NO}(\rho) e^{i\varphi})$. $\beta = 0.9$
• Figure 4: A numerical simulation of the interaction between two parallel semilocal strings with different 'colour', from Ref. AchKuiPerVac92. The initial configuration has one string with $\Phi_1^T = (0, f(\rho_1) e^{i\varphi_1} )$ and the other with $\Phi_2^T = (if(\rho_2) e^{i\varphi_2}, 0)$, where $(\rho_i, \varphi_i)$ are polar coordinates centred at the cores of each string. The energy density of the string pair is plotted in the plane perpendicular to the strings. The colour difference is radiated away in the form of Goldstone bosons, and the strings cores remain at their initial positions. $\beta = 0.5$.
• Figure 5: Loop formation from semilocal string segments. The figure shows two snapshots, at $t = 70$ and $t = 80$, of a $64^3$ numerical simulation of a network of semilocal strings with $\beta = 0.05$ from Ref.AchBorLid98, where the ends of an open segment of string join up to form a closed loop (see section \ref{['networks']} for a discussion of the simulations). Subsequently the loops seem to behave like those of topological cosmic string, contracting and disappearing.