Matching conditions and duality in N=1 SUSY gauge theories in the conformal window

We discuss duality in N=1 SUSY gauge theories in Seiberg’s conformal window, 3N_e/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 α corrections. The conserved (anomaly-free) R current is built to all orders in α. Although this current contains all orders in α 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.