BRS and Anti-BRS Symmetry in Topological Yang--Mills Theory

TL;DR

This paper enhances the understanding of topological Yang--Mills theory by incorporating both BRS and anti-BRS symmetries, revealing its geometric structure and connections to ordinary Yang--Mills theory.

Contribution

It introduces a formalism that includes anti-BRS symmetry, clarifies the geometric interpretation, and uncovers a triality symmetry in topological Yang--Mills theory.

Findings

Clear geometric meaning in superspace connections and curvatures

Discovery of SU(3) triality symmetry

Recovery of standard gauge-fixed action from the formalism

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 spacetime, and the two ghost directions of superspace. Finally, we demonstrate how to recover the usual gauge-fixed topological Yang--Mills action from our formalism.