Exact Scale Invariance of the BF-Yang-Mills Theory in Three Dimensions

TL;DR

This paper proves that the extended BF-Yang-Mills theory in three dimensions, including a scalar field, is ultraviolet finite with all beta-functions and anomalous dimensions vanishing, based on an anomaly-free trace identity.

Contribution

It demonstrates the exact scale invariance of the 3D extended BF-Yang-Mills theory through a rigorous all-orders proof.

Findings

The theory is ultraviolet finite.

All beta-functions vanish.

The trace identity is anomaly-free.

Abstract

The ``extended'' BF-Yang-Mills theory in 3 dimensions, which contains a minimally coupled scalar field, is shown to be ultraviolet finite. It obeys a trivial Callan-Symanzik equation, with all beta-functions and anomalous dimensions vanishing. The proof is based on an anomaly-free trace identity valid to all orders of perturbation theory.