Topological Yang-Mills Theory with Two Fermionic Charges. A Superfield Approach on K\"ahler Manifolds

• Main Authors: Dahmen, H. D, Marculescu, S, Portmann, T
• Format: Journal Article
• Language: English
• Published: 23-06-1995
• Subjects: Physics - High Energy Physics - Theory
• DOI: 10.48550/arxiv.hep-th/9506162

Nucl.Phys. B462 (1996) 493-523 The four-dimensional topological Yang-Mills theory with two anticommuting
charges is naturally formulated on K\"ahler 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.