Cohomology of the variational complex in BRST theory

TL;DR

This paper establishes that the cohomology of the variational complex in BRST theory matches the de Rham cohomology of the underlying manifold, linking physical gauge theories with topological invariants.

Contribution

It proves the equivalence between the variational complex cohomology in BRST theory and de Rham cohomology on any manifold, providing a topological insight into gauge theories.

Findings

Cohomology of the variational complex equals de Rham cohomology.

Applicable to arbitrary manifolds in BRST theory.

Links gauge theory cohomology to topological invariants.

Abstract

We show that cohomology of the variational complex in field-antifield BRST theory on an arbitrary manifold is equal to the de Rham cohomology of this manifold.