Quantum Chromodynamics with Many Flavors

Abstract

We investigate the phase structure of lattice QCD for general number of flavors $N_F$. Based on numerical data combined with the results of the perturbation theory we propose the following picture: When $N_F\ge 17$, 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 $16\ge N_F\ge 7$, 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 $N_F\le 6$.

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.]