Topological Yang-Mills Theory with Two Fermionic Charges. A Superfield Approach on Kähler Manifolds

Abstract

The four-dimensional topological Yang-Mills theory with two anticommuting charges is naturally formulated on Kähler manifolds. By using a superspace approach we clarify the structure of the Faddeev-Popov sector and determine the total action. This enables us to perform perturbation theory around any given instanton configuration by manifestly maintaining all the symmetries of the topological theory. The superspace formulation is very useful for recognizing a trivial observable (i.e. having vanishing correlation functions only) as the highest component of a gauge invariant superfield. As an example of non-trivial observables we construct the complete solution to the simultaneous cohomology problem of both fermionic charges. We also show how this solution has to be used in order to make Donaldson's interpretation possible.

41 pages, LaTeX. Section about Donaldson cohomology revised and completed. To be published in Nucl. Phys. B

References in corpus (12)

• 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
• Supersymmetric Yang-Mills Theory On A Four-Manifold
• On S-Duality in Abelian Gauge Theory
• Localisation of the Donaldson's invariants along Seiberg-Witten classes
• Topological Matter in Four Dimensions
• Holomorphic Yang-Mills Theory on Compact Kähler Manifolds
• N=2 Topological Yang-Mills Theory on Compact Kähler Surfaces
• Topological field theory and physics
• Anomalies in Instanton Calculus
• Notes on Seiberg-Witten Gauge Theory