Intercommutation of Semilocal Strings and Skyrmions

Pablo Laguna

Department of Astronomy & Astrophysics, IGPG, CGWP
Penn State University, University Park, PA 16802

Vishnu Natchu and Richard A. Matzner

Center for Relativity, Department of Physics
The University of Texas at Austin, Austin, TX 78712

Tanmay Vachaspati

CERCA, Department of Physics
Case Western Reserve University,10900 Euclid Avenue, Cleveland, OH 44106-7079


We study the intercommuting of semilocal strings and Skyrmions, for a wide range of internal parameters, velocities and intersection angles by numerically evolving the equations of motion. We find that the collisions of strings and strings, strings and Skyrmions, and Skyrmions and Skyrmions, all lead to intercommuting for any set of parameters. Even the collisions of unstable Skyrmions and strings leads to intercommuting, demonstrating that the phenomenon of intercommuting is very robust, extending to dissimilar field configurations that are not stationary solutions. Even more remarkably, at least for the semilocal  formulation considered here, all intercommutations trigger a reversion to U(1) Nielsen-Olesen strings.

Movies of Simulations:
Movies are generated as isometric views with the camera at 45 degress elevation and 45 degree rotation about the z axis.
Click on the images to access the movie files.

Figure 1: Field $\sigma $ for a collision of q_0= 1 ("top") and $q_0$=3 semilocal strings, at $\Theta = 90^\circ $, with collision velocity V= 0.9. The contours are $1-\vert \sigma \vert^2 $ at values 0.1, 0.2, 0.5. Note that $\vert\sigma \vert^2 + \vert \phi \vert ^2 = 1 $ is the vacuum. The strings reconnect.
\scalebox{0.40}{\includegraphics{phi0.eps}} \scalebox{0.40}{\includegraphics{phi1.eps}}

Figure 2: Coincident configurations of the field $\phi $ in the collision of FIG 1. The contours are $\vert\phi \vert^2$ at 0.2, 0.3, 0.5. The value $\phi = 0$ is an NO string. It can be seen that the configurations reverts to NO form after the collision. This is in spite of the fact our boundary conditions hold the boundary values of the strings in their original $q_0$=1 and $q_0$=3 state. The transition from the initial value of $\phi $ to the value of zero means we have two NO strings near the center terminating on the (outward moving) ends of the $q\ne 0$ semilocal strings.
\scalebox{0.40}{\includegraphics{psi0.eps}} \scalebox{0.40}{\includegraphics{psi1.eps}}

Movie simulations for other parameter values can be viewed below
q (top string) = 0.0 q (top string) = 1.0
q (bottom string) = 0.0 X X
q (bottom string) = 1.0