Quantum Chromodynamics with Many Flavors∗)

We investigate the phase structure of lattice QCD for general number of flavors NF . Based on numerical data combined with the results of the perturbation theory we propose the following picture: When NF ≥ 17, there is only one IR fixed point at vanishing gauge coupling, i.e., the theory in the continuum limit is trivial. On the other hand, when 16 ≥ NF ≥ 7, there is a non-trivial fixed point. Therefore, the theory is non-trivial with anomalous dimensions, however, without quark confinement. Theories which satisfy both quark confinement and spontaneous chiral symmetry breaking in the continuum limit exist only for NF ≤ 6. ∗) Talk presented by K. Kanaya at the 1997 Yukawa International Seminar (YKIS’97) on “NonPerturbative QCD — Structure of the QCD Vacuum —”, YITP, Kyoto, Japan, 2–12 Dec. 1997. To be published in the proceedings [Prog. Theor. Phys. Suppl.]. 1 typeset using PTPTEX.sty