Monopoles and Four-Manifolds

Abstract

Recent developments in the understanding of $N=2$ supersymmetric Yang-Mills theory in four dimensions suggest a new point of view about Donaldson theory of four manifolds: instead of defining four-manifold invariants by counting $SU(2)$ instantons, one can define equivalent four-manifold invariants by counting solutions of a non-linear equation with an abelian gauge group. This is a ``dual'' equation in which the gauge group is the dual of the maximal torus of $SU(2)$. The new viewpoint suggests many new results about the Donaldson invariants.

29 pp, harvmac

References in corpus (1)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory

Cited by in corpus (27)

• Duality Transformations in Supersymmetric Yang-Mills Theories coupled to Supergravity,
• On the Floer homology of plumbed three-manifolds
• Topological Reduction of 4D SYM to 2D $\sigma$--Models
• Introduction to Seiberg-Witten Theory and its Stringy Origin
• N=2 supersymmetric dynamics for pedestrians
• Couplings of self-dual tensor multiplet in six dimensions
• Blow-up of generalized complex 4-manifolds
• Gauged Hyperinstantons and Monopole Equations
• A TOPOLOGICAL LAGRANGIAN FOR MONOPOLES ON FOUR-MANIFOLDS
• Product Formulae for Ozsvath-Szabo 4-manifold Invariants
• Einstein metrics and smooth structures
• An SO(3)-monopole cobordism formula relating Donaldson and Seiberg-Witten invariants
• On the geometrization of matter by exotic smoothness
• The Vafa-Witten Theory for Gauge Group SU(N)
• PU(2) monopoles and links of top-level Seiberg-Witten moduli spaces
• A splitting theorem for the Seiberg-Witten invariant of a homology $S^1\times S^3$
• PU(2) monopoles. II: Top-level Seiberg-Witten moduli spaces and Witten's conjecture in low degrees
• PU(2) monopoles and a conjecture of Marino, Moore, and Peradze
• Knotting corks
• Einstein Metrics and Mostow Rigidity
• String Theory Symmetries
• $S$-duality in Vafa-Witten theory for non-simply laced gauge groups
• Holomorphic Yang-Mills Theory and Variation of the Donaldson Invariants
• A vanishing result for a Casson-type instanton invariant
• Virtual Morse-Bott index, moduli spaces of pairs, and applications to topology of smooth four-manifolds
• On path integral localization and the Laplacian, the thesis
• A lift of the Seiberg-Witten equations to Kaluza-Klein 5-manifolds