Non-Abelian Berry Phases and BPS Monopoles

Details Non-Abelian Berry Phases and BPS Monopoles Non-Abelian Berry Phases and BPS Monopoles

2008-09-23

arxiv.org/abs/0809.3783v3

Phys.Rev.Lett.102:191801,2009

Physics

High Energy Physics

High Energy Physics - Theory

15 pages. v2: footnotes added to point the reader towards later developments where conjectures made in this paper were subsequ

Scientific paper

10.1103/PhysRevLett.102.191801

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.

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