Fermions on the Electroweak String

Abstract

We construct a simple class of exact solutions of the electroweak theory including the naked $Z$--string and fermion fields. It consists in the $Z$--string configuration ($\varphi ,Z_{\theta }$), the {\it time} and $z$ components of the neutral gauge bosons ($Z_{0,3},A_{0,3}$) and a fermion condensate (lepton or quark) zero mode. The $Z$--string is not altered (no feed back from the rest of fields on the $Z$--string) while fermion condensates are zero modes of the Dirac equation in the presence of the $Z$--string background (no feed back from the {\it time} and $z$ components of the neutral gauge bosons on the fermion fields). For the case of the $n$--vortex $Z$--string the number of zero modes found for charged leptons and quarks is (according to previous results by Jackiw and Rossi) equal to $|n|$, while for (massless) neutrinos is $|n|-1$. The presence of fermion fields in its core make the obtained configuration a superconducting string, but their presence (as well as that of $Z_{0,3},A_{0,3}$) does not enhance the stability of the $Z$--string.

12 text pages (Latex) and 8 postscript figures in a uuencoded file

References in corpus (6)

• Detailed Stability Analysis of Electroweak Strings
• Electroweak Baryogenesis with Electroweak Strings
• Cosmic Strings and Electroweak Baryogenesis
• Topologically Stable Electroweak Flux Tube
• Stability of an electroweak string with a fermion condensate
• Stable, Spinning Embedded Vortices

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• Stable $Z$-strings with topological polarization in two Higgs doublet model
• Topological Defects in the Georgi-Machacek Model
• Perturbed Electroweak Strings and Fermion Zero Modes
• Brane Realization of Nambu Monopoles and Electroweak Strings
• Effect of Quark Scatter on Baryogenesis by Electroweak Strings
• Neutrino zeromodes on electroweak strings in light of topological insulators