Non-abelian monopoles and vortices

Abstract

The Seiberg-Witten equations are defined on certain complex line bundles over smooth oriented four manifolds. When the base manifold is a complex Kahler surface, the Seiberg-Witten equations are essentially the Abelian vortex equations. Using known non-abelian generalizations of the vortex equations as a guide, we explore some non-abelian versions of the Seiberg-Witten equations. We also make some comments about the differences between the vortex equations that have previously appeared in the literature and those that emerge as Kahler versions of Seiberg-witten type equations.

Revised version, in which some minor clarrifications and a number of unjustly ommitted references have been added. (Apologies to any inadvertantly offended parties.) To appear in the Proceedings of the 1995 Aarhus Conference in Geometry and Physics. 25 pages. AMSLaTeX v 2.09

References in corpus (5)

• Algebraic surfaces and Seiberg-Witten invariants
• Stable pairs on curves and surfaces
• Localisation of the Donaldson's invariants along Seiberg-Witten classes
• Quaternionic Monopoles
• The Coupled Seiberg-Witten Equations, vortices, and Moduli spaces of stable pairs

Cited by in corpus (15)

• Noncommutative Instantons in Higher Dimensions, Vortices and Topological K-Cycles
• Symplectic and Hyperkahler structures in a dimensional reduction of the Seiberg-Witten equations with a Higgs field
• Seiberg-Witten monopoles with multiple spinors on a surface times a circle
• Topological correlators of $SU(2)$, $\mathcal{N}=2^{\ast }$ SYM on four-manifolds
• On higher rank instantons & the monopole cobordism program
• Supersymmetric Gauge Theories, Vortices and Equivariant Cohomology
• Supersymmetric sigma models, gauge theories and vortices
• On the Riemannian geometry of Seiberg-Witten moduli spaces
• Duality and Topological Quantum Field Theory
• Duality in the Context of Topological Quantum Field Theory
• Donaldson Wall-Crossing Invariants Via Topology
• Virtual Morse-Bott index, moduli spaces of pairs, and applications to topology of smooth four-manifolds
• BPS center vortices in nonrelativistic SU(N) gauge models with adjoint Higgs fields
• The stable homotopy theory of vortices on Riemann surfaces
• $PU(N)$ monopoles, higher rank instantons, and the monopole invariants