Comments on the Equivalence between Chern-Simons Theory and Topological Massive Yang-Mills Theory in 3D

TL;DR

This paper investigates the quantum equivalence between Chern-Simons theory and topological massive Yang-Mills theory in 3D, demonstrating that their Green functions are independent of the gauge connection redefinition parameter due to BRST symmetry.

Contribution

It provides a quantum-level analysis of the classical equivalence, deriving the BRST differential, proving anomaly-free Slavnov-Taylor identities, and clarifying the role of ghost fields in the equivalence.

Findings

Green functions are independent of the gauge connection parameter.

Slavnov-Taylor identities are anomaly-free.

Ghost fields are essential for identifying physical states.

Abstract

The classical formal equivalence upon a redefinition of the gauge connection between Chern-Simons theory and topological massive Yang-Mills theory in three-dimensional Euclidean space-time is analyzed at the quantum level within the BRST formulation of the Equivalence Theorem. The parameter controlling the change in the gauge connection is the inverse $\lambda$ of the topological mass. The BRST differential associated with the gauge connection redefinition is derived and the corresponding Slavnov-Taylor (ST) identities are proven to be anomaly-free. The Green functions of local operators constructed only from the ($\lambda$-dependent) transformed gauge connection, as well as those of BRST invariant operators, are shown to be independent of the parameter $\lambda$, as a consequence of the validity of the ST identities. The relevance of the antighost-ghost fields, needed to take into account at the quantum level the Jacobian of the change in the gauge connection, is analyzed. Their role in the identification of the physical states of the model within conventional perturbative gauge theory is discussed.