Observables in Topological Yang-Mills Theories

TL;DR

This paper explores the definition and calculation of observables in topological Yang-Mills theories using a superspace approach, connecting to Donaldson-Witten invariants.

Contribution

It introduces a superspace formulation for topological field theories that systematically determines all observables via bi-descent equations.

Findings

Derived superspace expressions for observables.

Reproduced Donaldson-Witten polynomials in a specific gauge.

Established a method to compute observables in topological Yang-Mills theories.

Abstract

Using topological Yang-Mills theory as example, we discuss the definition and determination of observables in topological field theories (of Witten-type) within the superspace formulation proposed by Horne. This approach to the equivariant cohomology leads to a set of bi-descent equations involving the BRST and supersymmetry operators as well as the exterior derivative. This allows us to determine superspace expressions for all observables, and thereby to recover the Donaldson-Witten polynomials when choosing a Wess-Zumino-type gauge.