Hopf instantons in Chern-Simons theory

Abstract

We study an Abelian Chern-Simons and Fermion system in three dimensions. In the presence of a fixed prescribed background magnetic field we find an infinite number of fully three-dimensional solutions. These solutions are related to Hopf maps and are, therefore, labelled by the Hopf index. Further we discuss the interpretation of the background field.

one minor error corrected, discussion of gauge fixing added, some references added

References in corpus (2)

• Exact static soliton solutions of 3+1 dimensional integrable theory with nonzero Hopf numbers
• Hypermagnetic Knots, Chern-Simons Waves and the Baryon Asymmetry

Cited by in corpus (9)

• Anomalous Magnetohydrodynamics
• Multiple zero modes of the Dirac operator in three dimensions
• Degeneracy of zero modes of the Dirac operator in three dimensions
• Probing large-scale magnetism with the Cosmic Microwave Background
• The spectrum of anomalous magnetohydrodynamics
• New Topological Structures of Skyrme Theory: Baryon Number and Monopole Number
• Hyperbolic vortices and Dirac fields in 2+1 dimensions
• Hypermagnetic knots and gravitational radiation at intermediate frequencies
• Magnetic Zero-Modes, Vortices and Cartan Geometry