The Geometric Phase in Supersymmetric Quantum Mechanics

TL;DR

This paper investigates the geometric phase in supersymmetric quantum mechanics, demonstrating how non-perturbative effects like instantons influence the Berry connection, which relates to monopole solutions.

Contribution

It provides the first explicit calculation of instanton corrections to the Berry connection in supersymmetric quantum mechanics, linking it to monopole configurations.

Findings

Non-renormalization theorem prevents perturbative corrections.

Instantons contribute to the Berry connection.

Berry connection corresponds to SU(2) monopole.

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.