Perturbative and non-pertrubative trace anomalies

TL;DR

This paper compares perturbative and non-perturbative definitions of trace anomalies in fermionic models, confirming their equivalence and emphasizing the importance of diffeomorphism invariance.

Contribution

It derives trace anomalies using Duff's perturbative formula and demonstrates their agreement with non-perturbative results, clarifying the physical interpretation.

Findings

Perturbative and non-perturbative trace anomalies coincide.

Diffeomorphism invariance is crucial for the validity of the approach.

The paper provides a physical interpretation of Duff's formula.

Abstract

We study the definition of trace anomalies for models of Dirac and Weyl fermions coupled to a metric and a gauge potential. While in the non-perturbative case the trace anomaly is the response of the effective action to a Weyl transformation, the definition in a perturbative approach is more involved. In the latter case we use a specific formula proposed by M.Duff, of which we present a physical interpretation. The main body of the paper consists in deriving trace anomalies with the above formula and comparing them with the corresponding non-perturbative results. We show that they coincide and stress the basic role of diffeomorphism invariance for the validity of the approach.