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arXiv · 0709.0731

The Geometric Phase in Supersymmetric Quantum Mechanics

Chris Pedder·Julian Sonner·David Tong
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Abstract

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 a non-renormalization theorem which prohibits the connection from receiving perturbative corrections. However, we show that it does receive corrections from BPS instantons. We compute the one-instanton contribution to the Berry connection for the massive CP^1 sigma-model as the potential is varied. This system has two ground states and the associated Berry connection is the smooth SU(2) 't Hooft-Polyakov monopole.

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Chris Pedder, Julian Sonner, David Tong. 2008-10-30. The Geometric Phase in Supersymmetric Quantum Mechanics. https://doi.org/10.1103/physrevd.77.025009

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