Abstract
We determine the anomaly associated to an arbitrary scaling of the fields in a quantum gauge theory without making use of the Fujikawa method. We show that this anomaly is dependent on the spin term present in the action and at one loop can be directly extracted from the spin contribution to the one loop effective action. Our results can be readily applied to any gauge theory, supersymmetric or not and agree with previous determination for supersymmetric gauge theories based on the Fujikawa method.
Highlights
Where Faμν is an Abelian gauge tensor, βðgÞ is the beta function of the coupling constant g, and θμμ is the trace of the symmetric energy-momentum tensor θμν
The scale anomaly [1,2,3,4,5,6] measures the behavior of the gauge theory under the scale transformation which includes the scaling of space-time and specific transformations for each field
It might be useful to determine the anomalous contribution to the theory given by only the arbitrary scaling of the fields
Summary
We determine the anomaly associated with an arbitrary scaling of the fields in a quantum gauge theory without making use of the Fujikawa method. We show that this anomaly is dependent on the spin term present in the action and at one loop can be directly extracted from the spin contribution to the one loop effective action. It might be useful to determine the anomalous contribution to the theory given by only the arbitrary scaling of the fields Such a scaling was used earlier for supersymmetric gauge theories in [7] to connect the holomorphic and the canonical coupling constants. We make the following change of variables of integration in the partition function: AaμðxÞ → Aaμ0ðx0Þ 1⁄4 AaμðxÞ − α1⁄2AaμðxÞ þ xρ∂ρAμðxÞ; ΨðxÞ → Ψ0ðx0Þ 1⁄4 ΨðxÞ − α
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