Enhanced global symmetry constraints on ϵ terms

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 (T. Appelquist, P.S. Rodrigues da Silva, F. Sannino, Phys. Rev. D 60 (1999) 116007). 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 ϵ 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.