Observables in Topological Theories: A Superspace Formulation

TL;DR

This paper introduces a superspace formulation for topological Yang-Mills theory, defining observables via BRST cohomology, offering a new perspective that links supersymmetry with topological invariants.

Contribution

It proposes an alternative definition of observables in topological Yang-Mills theory using superspace and BRST cohomology, expanding the theoretical framework.

Findings

General solution of the BRST cohomology in superspace provided

Connects BRST invariance with super Yang-Mills invariance

Offers a new approach to understanding topological observables

Abstract

Observables of topological Yang-Mills theory were defined by Witten as the classes of an equivariant cohomology. We propose to define them alternatively as the BRST cohomology classes of a superspace version of the theory, where BRST invariance is associated to super Yang-Mills invariance. We provide and discuss the general solution of this cohomology.