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.
Cite
@article{arxiv.0709.0731,
title = {The Geometric Phase in Supersymmetric Quantum Mechanics},
author = {Chris Pedder and Julian Sonner and David Tong},
journal= {arXiv preprint arXiv:0709.0731},
year = {2008}
}
Comments
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