Quantum Chromodynamics with Many Flavors

We investigate the phase structure of lattice QCD for general number offlavors $N_F$. Based on numerical data combined with the results of theperturbation theory we propose the following picture: When $N_F \ge 17$, thereis only one IR fixed point at vanishing gauge coupling, i.e., the theory in thecontinuum limit is trivial. On the other hand, when $16 \ge N_F \ge 7$, thereis a non-trivial fixed point. Therefore, the theory is non-trivial withanomalous dimensions, however, without quark confinement. Theories whichsatisfy both quark confinement and spontaneous chiral symmetry breaking in thecontinuum limit exist only for $N_F \le 6$.Comment: Talk presented by K. Kanaya at the 1997 Yukawa International Seminar (YKIS'97) on ``Non-Perturbative QCD --- Structure of the QCD Vacuum ---'', YITP, Kyoto, Japan, 2--12 Dec. 1997. To be published in the proceedings [Prog. Theor. Phys. Suppl.