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 γ(N^{*}_{f})=1, where γ is the critical exponent. This result is incompatible with the existence of an analogue of Seiberg dual free magnetic phase in QCD. Using the BanksZaks 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.
 Publication:

Physical Review D
 Pub Date:
 January 2002
 DOI:
 10.1103/PhysRevD.65.021701
 arXiv:
 arXiv:hepph/0009272
 Bibcode:
 2002PhRvD..65b1701G
 Keywords:

 12.38.Aw;
 11.10.Hi;
 11.25.Hf;
 11.30.Pb;
 General properties of QCD;
 Renormalization group evolution of parameters;
 Conformal field theory algebraic structures;
 Supersymmetry;
 High Energy Physics  Phenomenology;
 High Energy Physics  Theory
 EPrint:
 10 pages, 1 figure, extended version of a talk given at the QCDNET2000 meeting, Paris, September 1114 2000