I am aware that in theories with spontaneous symmetry breaking, Magnetic Monopoles can exist as topological solitons. Can the same be done with the Standard Model gauge group. I am familiar with the contents of 't Hooft's paper Magnetic Monopoles in Unified Gauge theories. But the analysis in that paper is done for the $\operatorname{SO}(3)$ gauge group.

Is there a similar analysis for the standard model gauge group? Does the discovery of Higgs particle imply the existence of magnetic monopoles as topological solitons, and magnetic charge being treated as a topological charge?


No, I believe the Standard Model does not predict monopoles as a result of symmetry breaking. This is because the symmetry breaking $\mathrm{SU(2)} \times \mathrm{U(1)} \rightarrow \mathrm{U(1)}$ does not allow for topological solitons to exist.

Edit: $\pi_2(\mathrm{SU(2)} \times \mathrm{U(1)}/\mathrm{U(1))}=\pi_2(S^3)=0$

Source: To be or not to be? Magnetic monopoles in non-abelian gauge theories by F. Alexander Bais

  • $\begingroup$ Interesting, Can you please elaborate the on the calculation of the Homotopy group.In specific Why is SU(2)*U(1)/U(1) The same as S3. $\endgroup$ – Prathyush Sep 8 '13 at 15:02
  • $\begingroup$ @Prathyush Unfortunately, I'm not sure ho to calculate this (I've read it in some sources, for instance arxiv.org/abs/hep-th/0407197). However, I would be very interested to know how to calculate this, so maybe anybody else could explain this or provide some references? $\endgroup$ – Hunter Sep 9 '13 at 16:44
  • 2
    $\begingroup$ I offered a bounty hopefully some one will notice. $\endgroup$ – Prathyush Sep 10 '13 at 3:13

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