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Semilocal Strings

Semilocal strings are `worms' of energy that can arise from a complex interaction of quantum matter and force fields during a phase transition. This can be in a condensed matter system - such as superfluid helium - or in the very early universe, during the fracturing of a unified force into its constituents. The result is a line-like region of space in which the phase transition has been prevented from occuring by a combination of the topology of the vacuum and the energetics of the quantum system.

The strings originate as open segments, with a north magnetic monopole on one end and a south monopole on the other. As with any magnet, like poles repel and unlike poles attract. When two oppositely-oriented ends meet the monopoles annihilate forming either a closed loop (if the ends belong to the same string) or a longer segment (if the ends belong to different strings). In the first case the string loops shrink under their own tension and rapidly disappear. In the second case, however, the strings build up into longer and longer objects, ultimately spanning the universe. This question of the disappearance or persistence of the strings motivated our simulations.

If semilocal strings do persist then they would be a possible source of the primordial density perturbations needed to seed the formation of the gravitationally bound astronomical objects we observe today - from planets to clusters and superclusters of galaxies. In certain models they would also provide a mechanism for baryogenesis, generating the slight asymmetry between matter and antimatter in the early universe that allows us to exist today.

Semilocal String Formation In 2 Dimensions

We began by investigating the behaviour of the strings in 2 dimensions, with the string axis forced to lie perpendicular to the simulation plane.  The following images are  of semilocal string formation on a periodic square lattice, and show the magnetic flux energy density over the simulation plane.

  • An mpg animation (400 Kb) of semilocal string formation in 2 dimensions is here .

A paper discussing these simulations, published in Physical Review, is available on the archive as hep-ph/9702368 .

Semilocal String Formation In 3 Dimensions

Using the Cray T3E supercomputer at the National Energy Research Scientific Computing Center (NERSC) we were able to perform full 3 dimensional simulations. The following images are of semilocal string formation on a periodic cubic lattice with 256 points on each side. They show isosurfaces of the flux energy density measured as a fraction of the theoretical peak value. Particular thanks are due to Kevin Campbell and Terry Ligocki of the NERSC Visualisation Group for all their help.

Image Sequences

  • The simulation in close up (t = 20 - 100, isosurface = 1/4) : normal and red-blue stereo (50 Kb jpg).
  • The full simulation volume (t = 20 - 100, isosurface = 1/4) : normal (100 Kb jpg).


  • Initial evolution (t = 1 - 20, isosurface = 1/32) : normal and red-blue stereo (0.5 Mb mpg).
  • Segment growth by connection (t = 20 - 200, isosurface = 1/4) :  normal and red-blue stereo (4.2 Mb mpg).
  • Loop production and decay (t = 20 - 200, isosurface = 1/4) :  normal and red-blue stereo (4.7 Mb mpg).
  • Tracking back through the simulation (t = 20 - 200, isosurface = 1/4) :  normal and red-blue stereo (3.5 Mb mpg).
  • The full simulation volume (t = 20 - 2000, isosurface = 1/2) : normal (6.8 Mb mpg).

Note that for the red-blue stereo images the red lens should be over your left eye. Stereo quality will depend heavily on the accuracy of your colour mapping.

Alternatively, rather than plotting an isosurface, we can use colour and opacity as measures of the flux density, which helps to conveys the physically correct notion of the semilocal strings condensing out of an initial low-level background flux.

Three papers discussing these simulations have been published, in Physical Review Letters, (hep-ph/9802306), in Physica B (hep-ph/9810459), and in ``Particles, Strings and Cosmology - PASCOS-98'', editor P. Nath, World Scientific 1999 (available here) .

This work has also been the subject of online articles by ABC news, Berkeley Lab (also carried by the University of California and UniSci online), Currents, The Daily Cal and the Bronx High School of Science, and print-only articles by Science News [Volume 154, October 1998] , Scientific Computing World [Issue 41, September 1998] , Science et Vie [Number 977, February 1999] and Konr@d [June/July 1999] .