BRS and anti-BRS symmetry in topological Yang-Mills theory

Abstract

We incorporate both BRS symmetry and anti-BRS symmetry into the quantisation of topological Yang-Mills theory. This refines previous treatments which consider only the BRS symmetry. Our formalism brings out very clearly the geometrical meaning of topological Yang-Mills theory in terms of connections and curvatures in an enlarged superspace; and its simple relationship to the geometry of ordinary Yang-Mills theory. We also discover a certain SU(3) triality between physical space-time, and the two ghost directions of superspace. Finally, we demonstrate how to recover the usual gauge-fixed topological Yang-Mills action from our formalism.