Electroweak Strings, Zero Modes and Baryon Number

The Dirac equations for leptons and quarks in the background of an electroweak $Z-$string have zero mode solutions. If two loops of electroweak string are linked, the zero modes on one of the loops interacts with the other loop via an Aharanov-Bohm interaction. The effects of this interaction are briefly discussed and it is shown that the fermions induce a baryon number on linked loops of $Z-$string. (Submitted to Proceedings of "Trends in Astrophysics" Conference, Stockholm, 1994.)Comment: LaTeX using espcrc2.sty (version 2.5) (hit return on error messages), 3 page

Detailed Stability Analysis of Electroweak Strings

We give a detailed stability analysis of the Z-string in the standard electroweak model. We identify the mode that determines the stability of the string and numerically map the region of parameter space where the string is stable. For $\sin^2 \theta_W = 0.23$, we find that the strings are unstable for a Higgs mass larger than 23GeV. Given the latest constraints on the Higgs mass from LEP, this shows that, if the standard electroweak model is realized in Nature, the existing vortex solutions are unstable.Comment: 18 pages plus one figure (not included but available upon request). To appear in Nuclear Physics

Band structure in classical field theory

Stability and instability bands in classical mechanics are well-studied in connection with systems such as described by the Mathieu equation. We examine whether such band structure can arise in classical field theory in the context of an embedded kink in 1+1 dimensions. The static embedded kink is unstable to perturbations but we show that if the kink is dynamic it can exhibit stability in certain parameter bands. Our results are relevant for estimating the lifetimes of various embedded defects and, in particular, loops of electroweak Z-string.Comment: 6 pages, 4 fig. Reference added, Fig. 3 updated with improved numerical code, minor comments added. Version to be published in Phys. Rev.

Zero Modes on Linked Strings

We study linked loops of string in the presence of bosonic condensates and fermionic zero modes on the strings. We find that the strings necessarily carry a current if the bosons have an Aharanov-Bohm interaction with the string. The fermionic case is analyzed in the context of the standard model where there are lepton and quark zero modes on $Z-$strings. Here we find that the fermionic ground state in the linked string background is lower than the ground state when the loops are unlinked but otherwise identical. As in the bosonic case, the $Z-$strings carry a non-vanishing electric current in the ground state. The baryon number of the linked configuration is found to agree with previous indirect results. We also evaluate the angular momentum, electromagnetic charge and baryonic three current on the linked $Z-$string configuration. Finally we point out a possible gravitational analogue of the linked string system.Comment: LaTeX, 27 text pages + 2 figures, Fig. 1 file fixe

Magnetic Fields in the Aftermath of Phase Transitions

The COSLAB effort has focussed on the formation of topological defects during phase transitions. Yet there is another potentially interesting signature of cosmological phase transitions, which also deserves study in the lab. This is the generation of magnetic fields during phase transitions. In particular, cosmological phase transitions that also lead to preferential production of matter over antimatter (``baryogenesis''), are expected to produce helical (left-handed) magnetic fields. The study of analogous processes in the lab can yield important insight into the production of helical magnetic fields, and the observation of such fields in the universe can be invaluable for both particle physics and cosmology.Comment: 9 pages. Contribution to the Royal Society Discussion Meeting ``Cosmology Meets Condensed Matter'', January 28-29, 200