Berry Phase and Supersymmetry

Abstract

We study the constraints of supersymmetry on the non-Abelian holonomy given by U=P exp(i\int A), the path-ordered exponential of a connection A. For theories with four supercharges, we show that A satisfies the tt* equations if it is a function of chiral multiplets. In contrast, when A is a function of vector multiplets, it satisfies the Bogomolnyi monopole equations. We describe applications of these results to the Berry connection in supersymmetric quantum mechanics.

10 pages. v2 and v3: typos fixed

References in corpus (8)

• Phases of $N=2$ Theories In Two Dimensions
• Quantum Quivers and Hall/Hole Halos
• Phases Of N=2 Theories In 1+1 Dimensions With Boundary
• The Berry Phase of D0-Branes
• The Geometric Phase in Supersymmetric Quantum Mechanics
• Non-Abelian Berry Phases and BPS Monopoles
• The Geometric Phase and Gravitational Precession of D-Branes
• Black Hole Berry Phase

Cited by in corpus (13)

• Topological Anti-Topological Fusion in Four-Dimensional Superconformal Field Theories
• Aspects of Berry phase in QFT
• The Geometric Phase in Supersymmetric Quantum Mechanics
• 3d $\mathcal{N}=4$ Gauge Theories on an Elliptic Curve
• Non-Abelian Berry Phases and BPS Monopoles
• N=4, 3D Supersymmetric Quantum Mechanics in Non-Abelian Monopole Background
• 4d partition function on S^1 x S^3 and 2d Yang-Mills with nonzero area
• Supersymmetric Ground States of 3d $\mathcal{N}=4$ Gauge Theories on a Riemann Surface
• Harmonic Superfields in N=4 Supersymmetric Quantum Mechanics
• Berry's connection, Kähler geometry and the Nahm construction of monopoles
• Non-Abelian Berry Phase, Instantons and N=(0,4) Supersymmetry
• Connection Constraints from Non-Abelian Supersymmetric Quantum Mechanics
• Extended supersymmetry and its applications in quantum mechanical models associated with self-dual gauge fields