The Geometric Phase in Supersymmetric Quantum Mechanics

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.Comment: 28 pages, 2 figures, references added. v2: clarification of possible corrections to Abelian Berry phase. v3: footnotes added to point the reader towards later development