Abstract
We explore the geometric phase in $\mathcal{N}=(2,2)$ supersymmetric quantum mechanics. The Witten index ensures the existence of degenerate ground states, resulting in a non-Abelian Berry connection. We exhibit a nonrenormalization 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 $C{P}^{1}$ 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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