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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.
Highlights
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
We use a specific formula proposed by M.Duff, of which we present a physical interpretation
Summary
We will consider two examples where these anomalies do appear: the even trace anomaly in the theory of a Dirac fermion, and the odd one in the theory of a Weyl fermion, both coupled to a vector potential Vμ. In both cases, we compare the results with the ones obtained via the non-perturbative heat-kernel-like method, which we refer to as the Seeley–DeWitt (SDW).
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