Non-Abelian Berry Phases and BPS Monopoles

@inproceedings{Sonner2008NonAbelianBP,
  title={Non-Abelian Berry Phases and BPS Monopoles},
  author={Julian Sonner and David Tong},
  year={2008}
}
We study a simple quantum mechanical model of a spinning particle moving on a sphere in the presence of a magnetic field. The system has two ground states. As the magnetic field is varied, the ground states mix through a non-Abelian Berry phase. We show that this Berry phase is the path ordered exponential of the smooth SU(2) ’t Hooft-Polyakov monopole. We further show that, by adjusting a potential on the sphere, the monopole becomes BPS and obeys the Bogomolnyi equations. For this choice of… 

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