Conformal Anomaly for Non-Conformal Scalar Fields

TL;DR

This paper proposes a new, finite, and local definition of conformal anomaly applicable to non-conformally invariant theories, demonstrated through a non-minimally coupled scalar field example.

Contribution

It introduces a general definition of conformal anomaly for non-Weyl invariant theories, aligning with heat kernel results for specific scalar fields.

Findings

Defined a finite, local conformal anomaly for non-conformal theories

Validated the definition with the non-minimally coupled scalar example

Showed consistency with heat kernel method results

Abstract

We give a general definition of the conformal anomaly for theories that are not classically Weyl invariant and show that this definition yields a quantity that is both finite and local. As an example we study the conformal anomaly for a non-minimally coupled massless scalar and show that our definition coincides with results obtained using the heat kernel method.