# 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…

## 6 Citations

### Geometric phase in supersymmetric quantum mechanics

- 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…

### Berry phase and supersymmetry

- 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…

### Connection Constraints from Non-Abelian Super symmetric QuantumMechanics

- Mathematics
- 2010

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…

### Berry’s connection, Kähler geometry and the Nahm construction of monopoles

- Mathematics
- 2015

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…

### Black hole Berry phase.

- PhysicsPhysical 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.

### Tunneling D0-branes

- Physics
- 2008

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 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…

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