Fixing the conformal window in QCD

Abstract

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 ``nonperturbative'' contributions below ${N}_{f}^{*}$ is suggested. Assuming an infrared fixed point persists in the perturbative part of the QCD coupling in some range below ${N}_{f}^{*}$ leads to the condition $\ensuremath{\gamma}{(N}_{f}^{*})=1,$ where $\ensuremath{\gamma}$ is the critical exponent. This result is incompatible with the existence of an analogue of Seiberg dual free magnetic phase 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, 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.