Algebraic Structures of Topological Yang-Mills Theory

TL;DR

This paper explores the algebraic structure of BRST symmetries in topological Yang-Mills theory, extending known formulas and descent equations, and proposing a non-Abelian anomaly analogue with explicit solutions.

Contribution

It introduces an extended BRST algebra and descent equations for topological Yang-Mills theory, generalizing previous analyses and proposing a new anomaly framework.

Findings

Extended BRST algebra and descent equations derived.

Explicit solutions of the extended descent equation calculated.

Proposed non-Abelian anomaly analogue in topological Yang-Mills theory.

Abstract

We discuss the algebraic structure of the various BRST symmetries associated with topological Yang-Mills theory as a generalization of the BRS analysis developed for the non-Abelian anomaly in the local Yang-Mills theory. We show that our BRST algebra leads to an extended {\it Russian formula\/} and {\it descent equations}, which contains the descent equation of Yang-Mills theory as sub-relations. We propose the non-Abelian anomaly counterpart in Topological Yang-Mills theory using the extended descent equation. We also discuss the geometrical structure of our BRST symmetry and some explicit solutions of the extended descent equation are calculated.