The Dynamics of Chern-Simons Vortices

Abstract

We study vortex dynamics in three-dimensional theories with Chern-Simons interactions. The dynamics is governed by motion on the moduli space M in the presence of a magnetic field. For Abelian vortices, the magnetic field is shown to be the Ricci form over M; for non-Abelian vortices, it is the first Chern character of a suitable index bundle. We derive these results by integrating out massive fermions and following the fate of their zero modes.

24 pages, 3 figures. v2: references added

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Cited by in corpus (19)

• Vortices and Impurities
• Non-Abelian Vortices in SO(N) and USp(N) Gauge Theories
• Non-Abelian Vortices at Weak and Strong Coupling in Mass Deformed ABJM Theory
• Non-Abelian Chern-Simons vortices with generic gauge groups
• A 5d/3d duality from relativistic integrable system
• Twisted Hilbert Spaces of 3d Supersymmetric Gauge Theories
• Fractional and semi-local non-Abelian Chern-Simons vortices
• The Moduli Space Metric for Well-Separated Non-Abelian Vortices
• Dynamics of Non-Abelian Vortices
• Monopoles and Wilson Lines
• Exact moduli space metrics for hyperbolic vortices
• Vortices and 3 dimensional dualities
• On the curvature of vortex moduli spaces
• Semionic Supersymmetric Solitons
• Ricci magnetic geodesic motion of vortices and lumps
• Chern-Simons deformation of vortices on compact domains
• Vortex counting and the quantum Hall effect
• Zero-modes of Non-Abelian Solitons in Three Dimensional Gauge Theories
• The moduli space of non-Abelian vortices in Yang-Mills-Chern-Simons-Higgs theory