Eur. Phys. J. C (2006) 45: 227-240
https://doi.org/10.1140/epjc/s2005-02382-x

Theoretical Physics

Observables in topological Yang-Mills theorieswith extended shift supersymmetry

¹ Universidade Federal do Espírito Santo (UFES), Av. Fernando Ferrari, 514, 29075-910, Vitória, ES, Brazil
² Scuola Internazionale Superiore di Studi Avanzati (SISSA), via Beirut 4, 34014, Trieste, Italia
³ Centro Brasileiro de Pesquisas Fsicas (CBPF), Rua Dr. Xavier Sigaud, 150, 22290-180, Rio de Janeiro, Brazil

^* e-mail: clisthen@cce.ufes.br

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.