${\cal N} = 1$ Euler Anomaly Flow from Dilaton Effective Action

TL;DR

This paper derives the change in the Euler anomaly coefficient for ${ m N}=1$ supersymmetric gauge theories using dilaton effective action techniques, connecting anomaly flow with conformal transformations and curved backgrounds.

Contribution

It provides a novel derivation of the Euler anomaly flow in ${ m N}=1$ theories via dilaton effective action and anomaly matching, linking RG flow to conformal anomaly differences.

Findings

Rederived $ riangle a$ for ${ m N}=1$ theories using dilaton effective action.

Established a one-to-one correspondence between $ riangle a$ and Wess-Zumino dilaton action.

Connected RG flow to conformal anomaly via curved background techniques.

Abstract

We consider ${\cal N} =1$ supersymmetric gauge theories in the conformal window. The running of the gauge coupling is absorbed into the metric by applying a suitable matter superfield- and Weyl-transformation. The computation becomes equivalent to one of a free theory in a curved background carrying the information of the renormalisation group flow. We use the techniques of conformal anomaly matching and dilaton effective action, by Komargodski and Schwimmer, to rederive the difference of the Euler anomaly coefficient $\Delta a \equiv a_{\rm UV} - a_{\rm IR} $ for the ${\cal N} =1$ theory. The structure of $\Delta a $ is therefore in one-to-one correspondence with the Wess-Zumino dilaton action.