Matching Conditions and Duality in N=1 SUSY Gauge Theories in the Conformal Window

TL;DR

This paper examines duality in N=1 supersymmetric gauge theories within the conformal window, analyzing 't Hooft consistency conditions with higher order corrections and confirming the validity of Seiberg's matching procedure.

Contribution

It provides a detailed analysis of 't Hooft anomaly matching conditions considering higher order corrections, supporting the robustness of Seiberg duality in the conformal window.

Findings

't Hooft conditions are one-loop for the anomaly-free R current.

Higher order α corrections do not alter the anomaly matching.

Electric and magnetic theories are inequivalent at short distances.

Abstract

We discuss duality in $N=1$ SUSY gauge theories in Seiberg's conformal window, $(3N_c/2)<N_f<3N_c$. The 't Hooft consistency conditions -- the basic tool for establishing the infrared duality -- are considered taking into account higher order $\alpha$ corrections. The conserved (anomaly free) $R$ current is built to all orders in $\alpha$. Although this current contains all orders in $\alpha$ the 't Hooft consistency conditions for this current are shown to be one-loop. This observation thus justifies Seiberg's matching procedure. We also briefly discuss the inequivalence of the ``electric" and ``magnetic" theories at short distances.