Conformal anomaly in a vector field model with auxiliary scalar field

TL;DR

This paper investigates the conformal anomaly in a gauge vector field model using an auxiliary scalar to preserve gauge symmetry and explores the resulting dynamics of this scalar after dimensional regularization.

Contribution

It introduces an auxiliary scalar field approach to analyze conformal anomalies in vector field models, maintaining gauge symmetry and examining the scalar's independent dynamics.

Findings

The auxiliary scalar gains independent dynamics in 4D limit.

The scalar exhibits interesting properties post-regularization.

The approach preserves gauge symmetry and avoids unitarity issues.

Abstract

The conformal anomaly has well-known ambiguities related to the possible schemes of regularization and renormalization. In case of dimensional regularization, one of the options is to formulate the theory as conformal in the dimension $D \neq 4$. For a gauge vector field this can be done in several ways and one of the options is to introduce an auxiliary scalar playing the role of a compensator. The advantage of this approach is that it preserves gauge symmetry and avoids problems with possible violation of unitarity. We explore the consequences of introducing such an auxiliary field for the anomaly and anomaly-induced action. It is shown that the new scalar degree of freedom gains an independent dynamics after taking the $4D$ limit. The remnant scalar, also, demonstrates some interesting properties.