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Fixing the conformal window in QCD

Georges Grunberg
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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 ``non-perturbative'' contributions to amplitudes below N_f^* is suggested. Assuming an infrared fixed point persists in the perturbative part of the QCD coupling even below N_f^* leads to the condition γ(N_f^*)=1, where γis the critical exponent. Using the Banks-Zaks expansion, one gets 4<N_f^*<6. This result is incompatible with the existence of an analogue of Seiberg duality in QCD. The presence of a negative ultraviolet fixed point is required both in QCD and in supersymmetric QCD to preserve causality within the conformal window. Evidence for the existence of such a fixed point in QCD is provided.

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Georges Grunberg. 2000-11-16. Fixing the conformal window in QCD. https://doi.org/10.1103/physrevd.65.021701

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