Flavor doubling and the nature of asymptopia

We consider the possibility that QCD with N flavors has a useful low-energy description with 2N flavors. Specifically, we investigate a free theory of 2N quarks. Although the free theory is U(N)(L)xU(N)(R) invariant, it admits a larger U(2N) invariance. However, when the axial anomaly is accounted for in the effective theory by a 't Hooft interaction, only SU(N)(L)xSU(N)(R)xU(1)(B) subset of U(2N) survives. There is, however, a residual discrete symmetry that is not a symmetry of the QCD lagrangian. This S-2 subgroup of U(2N) has many interesting properties. For instance, when explicit chiral symmetry breaking effects are present, S-2 is broken unless <(theta)over bar>=0 or pi. By expressing the free theory on the light-front, we show that flavor doubling implies several superconvergence relations in pion-hadron scattering. Implicit in the 2N-flavor effective theory is a Regge trajectory with vacuum quantum numbers and unit intercept whose behavior is constrained by S-2. In particular, S-2 implies that forward pion-hadron scattering becomes purely elastic at high energies, in good agreement with experiment. (C) 1998 Academic Press.