  Recently it has been proposed that the physical spectrum of a vector-like
gauge field theory may exhibit an enhanced global symmetry near a
chiral/conformal phase transition. The new symmetry is related to the
possibility, supported by various investigations, that a parity-doubled
spectrum develops as the number of fermions Nf is increased to a critical value
above which it is expected that the symmetric phase is restored.
  We show that parity-doubling together with the associated enhanced global
symmetry severely constrains the epsilon terms of the effective Lagrangian
involving Goldstone bosons as well as massive spin-1 particles. We extend our
analysis to underlying fermions in pseudo-real representations of the gauge
group.
