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.

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

References in corpus (22)

• Phases of $N=2$ Theories In Two Dimensions
• Holonomic Quantum Computation
• Aspects of N=2 Supersymmetric Gauge Theories in Three Dimensions
• SU(2) Non-Abelian Holonomy and Dissipationless Spin Current in Semiconductors
• Non-Abelian Berry connections for quantum computation
• Quantum Quivers and Hall/Hole Halos
• Branes and N=2 Theories in Two Dimensions
• TASI Lectures on Solitons
• The Moduli Space of BPS Domain Walls
• Instantons, Three-Dimensional Gauge Theory, and the Atiyah-Hitchin Manifold
• Five-branes in M(atrix) Theory
• The Power of Holomorphy -- Exact Results in 4D SUSY Field Theories
• Exact Results for Supersymmetric Sigma Models
• A Non-Renormalization Theorem for the d=1, N=8 Vector Multiplet
• The BPS Spectra of Two-Dimensional Supersymmetric Gauge Theories with Twisted Mass Terms
• Non-Abelian Holonomy of BCS and SDW Quasi-particles
• An Index Theorem for Domain Walls in Supersymmetric Gauge Theories
• Berry Phase and Supersymmetry
• Non-Abelian Berry Phases and BPS Monopoles
• Non-abelian Berry's phase and Chern numbers in higher spin pairing condensates
• The Geometric Phase and Gravitational Precession of D-Branes
• Perturbative Quantum Corrections to the Supersymmetric CP^1 Kink with Twisted Mass

Cited by in corpus (16)

• Topological Anti-Topological Fusion in Four-Dimensional Superconformal Field Theories
• The chiral ring of AdS3/CFT2 and the attractor mechanism
• The Berry Phase of D0-Branes
• 3d $\mathcal{N}=4$ Gauge Theories on an Elliptic Curve
• Berry Phase and Supersymmetry
• Non-Abelian Berry Phases and BPS Monopoles
• 4d partition function on S^1 x S^3 and 2d Yang-Mills with nonzero area
• The Geometric Phase and Gravitational Precession of D-Branes
• Supersymmetric Ground States of 3d $\mathcal{N}=4$ Gauge Theories on a Riemann Surface
• Non-Abelian Monopole in the Parameter Space of Point-like Interactions
• Noncyclic geometric phases and helicity transitions for neutrino oscillations in a magnetic field
• Extended supersymmetry with central charges in Dirac action with curved extra dimensions
• Extended supersymmetry with central charges in higher dimensional Dirac action
• Tunneling D0-branes
• Connection Constraints from Non-Abelian Supersymmetric Quantum Mechanics
• Supersymmetry and non-Abelian geometric phase for a free particle on a circle with point-like interactions