BRS Cohomology of Zero Curvature Systems I. The Complete Ladder Case

TL;DR

This paper introduces a zero curvature formalism based on BRS cohomology for a broad class of field theories, simplifying the solution of consistency conditions, with applications to topological theories and string ghost systems.

Contribution

It develops a comprehensive zero curvature approach using BRS cohomology, providing new tools for analyzing field theories with topological and string ghost systems.

Findings

Formalism simplifies solving Wess-Zumino consistency conditions.

Applicable to topological theories and B-C string ghost systems.

Provides detailed examples demonstrating the method's utility.

Abstract

We present here the zero curvature formulation for a wide class of field theory models. This formalism, which relies on the existence of an operator $\d$ which decomposes the exterior space-time derivative as a BRS commutator, turns out to be particularly useful in order to solve the Wess-Zumino consistency condition. The examples of the topological theories and of the $B$-$C$ string ghost system are considered in detail.