2007/09/30 by Chris Pedder, Julian Sonner, David Tong
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Connection (principal bundle) #Degenerate energy levels #Geometric phase #Geometry #Instanton #Magnetic monopole #Mathematical physics #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Quantum statistical mechanics #Supersymmetric quantum mechanics #Theoretical physics #hep-th
paper · pdf · doi:10.1103/physrevd.77.025009
published as Phys.Rev.D77:025009,2008 · 28 pages, 2 figures, references added. v2: clarification of possible corrections to Abelian Berry phase. v3: footnotes added to point the reader towards later developments
openalex publication_date 2008/01/11 · arxiv created 2008/10/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 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 CP1 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.