Electroweak String

Background

Electroweak strings are `worms' of energy which are formed due to the complex interaction of the scalar and gauge fields in a phase transition in the SU(2) x U(1) bosonic sector of the Glashow-Salam-Weinberg model of electroweak physics. Like any defect, these strings correspond to regions of space where the phase transition has been frustrated. If we remove the SU(2) gauge fields, this system reduces to the so-called semilocal strings examined in our previous work.

The additional gauge fields visibly increase the complexity of the system. Now, as well as the line-like strings we also see ball-like magnetic monopoles, with a monopole-antimonopole pair occuring at the ends of the strings. A string with monopoles at the ends is called, for obvious reasons, a dumbbell.

Many such dumbbells form in the phase transition, and while some of them collapse and disappear, others grow by joining to a neighbour. The relative likelihoods of these two modes of evolution depend on the parameters of the model - specifically the ratio of the Higgs and Z-boson masses, and the weak mixing angle. As we vary these parameters, identical initial field configurations will evolve into a persistent or non-persistent string network. Part of the purpose of this work is to establish the line in this 2-parameter space dividing persistence from non-persistence.

Although our results indicate that the actual observed values of the electroweak theory parameters are well outside the persistent regime, we have also shown that non-topological defects per se do form and can persist, and must be taken into account when other phase transitions are studied.
 

Simulation Images

These images show the A and Z fields at three times during two simulations with the same initial field configurations but with slightly different field coupling parameters yielding persistent and non-persistent electroweak string networks.
 

Persistent configuration		Non-persistent configuration
	t = 50
	t = 200
	t = 300

Downloadable mpeg movies of electroweak string evolution

Our largest simulation of electroweak string formation and evolution on a 256x256x256 periodic cubic lattice, showing isosurfaces of the A and Z fields, is available at high (10 Mb) and low (4.5 Mb) temporal resolution.

Our smaller (64x64x64) simulations

1. show isosurfaces of the A and Z fields here (3.5 Mb), and of the A and Higgs fields here (3.5 Mb), confirming that the Z and Higgs fields shadow each other as expected.
2. show isosurfaces of the A and Z fields in an alternative formulation of the initial conditions here (3.5 Mb), demonstrating the qualitative insensitivity of the results to the choice of initial condition algorithm.