Conformal window and Landau singularities

A physical characterization of Landau singularities is emphasized, which should trace the lower boundary N∗ f of the conformal window in QCD and supersymmetric QCD. A natural way to disentangle “perturbative” from “non-perturbative” contributions below N∗ f is suggested. Assuming an infrared fixed point is present in the perturbative part of the QCD coupling even in some range below N∗ f leads to the condition γ(N∗ f ) = 1, where γ is the critical exponent. This result is incompatible with the existence of an analogue of Seiberg duality in QCD. Using the Banks-Zaks expansion, one gets 4 ≤ N∗ f ≤ 6. The low value of N∗ f gives some justification to the infrared finite coupling approach to power corrections, and suggests a way to compute their normalization from perturbative input. If the perturbative series are still asymptotic in the negative coupling region, the presence of a negative ultraviolet fixed point is required both in QCD and in supersymmetric QCD to preserve causality within the conformal window. Some evidence for such a fixed point in QCD is provided through a modified Banks-Zaks expansion. Conformal window amplitudes, which contain power contributions, are shown to remain generically finite in the Nf → −∞ one-loop limit in simple models with infrared finite perturbative coupling. ∗Research supported in part by the EC program “Training and Mobility of Researchers”, Network “QCD and Particle Structure”, contract ERBFMRXCT980194.