# 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}
}
• 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…
6 Citations
• Physics
• 2008
We explore the geometric phase in N=(2,2) supersymmetric quantum mechanics. The Witten index ensures the existence of degenerate ground states, resulting in a non-Abelian Berry connection. We exhibit
• Physics
• 2009
We study the constraints of supersymmetry on the non-Abelian holonomy given by U = Pexp (i∫A), the path-ordered exponential of a connection A. For theories with four supercharges, we show that A
We generalise the study of constraints imposed by supersymmetry on the Berry connection to transformations with component elds in representations of an internal symmetry group G. Since the elds act
A bstractWe study supersymmetric deformations of N=4$$\mathcal{N}=4$$ quantum mechanics with a Kähler target space admitting a holomorphic isometry. We show that the twisted mass deformation
• Physics
Physical review letters
• 2009
This work argues that under adiabatic variations of the background values of the supergravity moduli, the quantum microstates of the black hole mix among themselves, and presents a simple example where this mixing is exactly computable, that of small supersymmetric black holes in 5 dimensions.
In the D0-D4-brane system, D0-branes do not tunnel. Instead, they form bound states with the D4-brane, whose ground states are exact. However, the D0-brane quantum mechanics contains a BPS instanton.

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We explore the geometric phase in N=(2,2) supersymmetric quantum mechanics. The Witten index ensures the existence of degenerate ground states, resulting in a non-Abelian Berry connection. We exhibit
• Physics
• 2009
We study the constraints of supersymmetry on the non-Abelian holonomy given by U = Pexp (i∫A), the path-ordered exponential of a connection A. For theories with four supercharges, we show that A
• Physics
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We study SU(2) Yang-Mills quantum mechanics with N = 2, 4, 8 and 16 supercharges. This describes the non-relativistic dynamics of a pair of D0-branes moving in d = 3, 4, 6 and 10 spacetime dimensions
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It is shown that the asymptotic form of the metric for the moduli space remains nonsingular for all values of the intermonopole distances and that it has the symmetries and other characteristics required of the exact metric.
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A quantal system in an eigenstate, slowly transported round a circuit C by varying parameters R in its Hamiltonian Ĥ(R), will acquire a geometrical phase factor exp{iγ(C)} in addition to the familiar