N=1 Euler Anomaly Flow from Dilaton Effective Action

Preprint number: CP3-Origins-2015-42 DNRF90 and DIAS-2015-42
Authors: Vladimir Prochazka (Edinburgh University) and Roman Zwicky (Edinburgh University & CP3-Origins)
External link: arXiv.org

We consider \(\mathcal{N}=1\) supersymmetric gauge theories in the conformal window.
The running of the gauge coupling is absorbed into the metric by applying a suitable matter-field and Weyl transformation. The theory becomes equivalent to
a free theory in a curved background carrying the information of the renormalisation group flow.
We use related technique of conformal anomaly matching and dilaton
effective action, by Komargodski and Schwimmer, to rederive the difference of the Euler anomaly coefficient $\Delta a = a_{UV} – a_{IR}$
for the \(\mathcal{N}=1\) theory thereby rederiving a well-known result.
The structure of $\Delta a$ is therefore in one-to-one correspondence with the Wess-Zumino dilaton term.