N = 1 Euler Anomaly from RG-dependent metric-Background

Preprint number: CP3-Origins-2016-53 DNRF90
Authors: Vladimir Prochazka (University of Edinburgh) and Roman Zwicky (University of Edinburgh & CP3-Origins & DIAS)
External link: arXiv.org

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We consider N = 1 supersymmetric gauge theories in the conformal window. By applying a suitable matter superfield- and Weyl-transformation the renormalisation group running of the theory is absorbed into the metric. The latter becomes a function of the Z-factor and the infrared anomalous dimension of the matter superfield. The Eu- ler flow ∆a ≡ aUV − aIR|N=1 becomes equivalent to a computation of a free theory with the non-trivial dynamics coming from expanding the Euler invariant in the flow depen- dent metric. The result is therefore directly obtained in terms of the infrared anomalous dimension confirming an earlier result using the matching of R-currents.