Observables in Topological Yang-Mills Theories With Extended Shift Supersymmetry

TL;DR

This paper classifies classical observables in topological Yang-Mills theories with extended shift supersymmetry, generalizing previous single-generator results through cohomology analysis.

Contribution

It provides a complete classification of observables for theories with multiple supersymmetry generators, extending Witten's equivariant cohomology framework.

Findings

Classifies BRST cohomology classes for extended supersymmetry

Generalizes known results to N-generator shift supersymmetry

Connects observables to solutions of an N-extended equivariant cohomology

Abstract

We present a complete classification, at the classical level, of the observables of topological Yang-Mills theories with an extended shift supersymmetry of N generators, in any space-time dimension. The observables are defined as the Yang-Mills BRST cohomology classes of shift supersymmetry invariants. These cohomology classes turn out to be solutions of an N-extension of Witten's equivariant cohomology. This work generalizes results known in the case of shift supersymmetry with a single generator.