An algebraic proof on the finiteness of Yang-Mills-Chern-Simons theory in D=3

TL;DR

This paper provides a rigorous algebraic proof that Yang-Mills-Chern-Simons theory in three dimensions remains finite at all perturbative orders, confirming its consistency and renormalizability.

Contribution

It introduces a trace identity equivalent to a local Callan-Symanzik equation, proving the vanishing of beta-functions and anomalous dimensions in the theory.

Findings

Proves all-order finiteness of the theory.

Establishes the validity of a trace identity at all loop orders.

Shows the vanishing of beta-functions and anomalous dimensions.

Abstract

A rigorous algebraic proof of the full finiteness in all orders of perturbation theory is given for the Yang-Mills-Chern-Simons theory in a general three-dimensional Riemannian manifold. We show the validity of a trace identity, playing the role of a local form of the Callan-Symanzik equation, in all loop orders, which yields the vanishing of the beta-functions associated to the topological mass and gauge coupling constant as well as the anomalous dimensions of the fields.