• DOI:10.1103/PhysRevLett.102.191801
• Corpus ID: 6512265

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}
}

• J. Sonner, D. Tong
• Published 23 September 2008
• Physics

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 potential, it turns out that there is a hidden supersymmetry underlying the system and the Bogomolnyi equations are analogous to the tt* equations of Cecotti and Vafa. We conjecture that the Bogomolnyi equations also govern the Berry phase of N = (2, 2) supersymmetric sigma models with other target spaces. ∗On leave from DAMTP and Trinity College, Cambridge, [e-mail]