Polynomial Invariants for SU(2) Monopoles

Abstract

We present an explicit expression for the topological invariants associated to $SU(2)$ monopoles in the fundamental representation on spin four-manifolds. The computation of these invariants is based on the analysis of their corresponding topological quantum field theory, and it turns out that they can be expressed in terms of Seiberg-Witten invariants. In this analysis we use recent exact results on the moduli space of vacua of the untwisted $N=1$ and $N=2$ supersymmetric counterparts of the topological quantum field theory under consideration, as well as on electric-magnetic duality for $N=2$ supersymmetric gauge theories.

50 pages, uses phyzzx.tex, a minor tex problem has been fixed

References in corpus (21)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• A Strong Coupling Test of S-Duality
• Exact Results on the Space of Vacua of Four Dimensional SUSY Gauge Theories
• Naturalness Versus Supersymmetric Non-renormalization Theorems
• Exact Superpotentials in Four Dimensions
• Phases of N=1 supersymmetric gauge theories in four dimensions
• Supersymmetric Yang-Mills Theory On A Four-Manifold
• ``Integrating in'' and exact superpotentials in 4d
• Twisted N=2 Supergravity as Topological Gravity in Four Dimensions
• Topological Sigma-Models in Four Dimensions and Triholomorphic Maps
• Quaternionic Monopoles
• Topological Matter in Four Dimensions
• Topological Twist in Four Dimensions, R-Duality and Hyperinstantons
• Gauged Hyperinstantons and Monopole Equations
• A TOPOLOGICAL LAGRANGIAN FOR MONOPOLES ON FOUR-MANIFOLDS
• Holomorphic Yang-Mills Theory on Compact Kähler Manifolds
• N=2 Topological Yang-Mills Theory on Compact Kähler Surfaces
• Non-Abelian Monopoles on Four-Manifolds
• Breaking of Topological Symmetry
• R-Symmetry and the Topological Twist of N=2 Effective Supergravities of Heterotic Strings

Cited by in corpus (15)

• Mathai-Quillen Formulation of Twisted N=4 Supersymmetric Gauge Theories in Four Dimensions
• Superconformal invariance and the geography of four-manifolds
• PU(2) monopoles and relations between four-manifold invariants
• The Vafa-Witten Theory for Gauge Group SU(N)
• Mass Perturbations in Twisted N=4 Supersymmetric Gauge Theories
• Topological twists of supersymmetric algebras of observables
• Duality in twisted N=4 supersymmetric gauge theories in four dimensions
• The General Decomposition Theory of SU(2) Gauge Potential, Topological Structure and Bifurcation of SU(2) Chern Density
• Duality in Topological Quantum Field Theories
• Twisted Baryon Number in N=2 Supersymmetric QCD
• N=2 Supersymmetric QCD and Four Manifolds; (I) the Donaldson and the Seiberg-Witten Invariants
• Donaldson-Witten Functions of Massless N=2 Supersymmetric QCD
• Topological gauge theories with antisymmetric tensor matter fields
• Duality in the Context of Topological Quantum Field Theory
• Higgs Bundles and Four Manifolds