Chiral symmetry breaking and the quark bilinear condensate in large-N QCD

We discuss spontaneous chiral symmetry breaking and the quark bilinear condensate in large-N-c quantum chromodynamics (QCD). It is known that the existence of the eta ' meson is implied in large-N-c QCD, as pointed out by Witten[] and Veneziano[]. First, we show that the existence of eta ' and the Ward-Takahashi identities implies the existence of Nambu-Goldstone bosons from chiral symmetry breaking SU(N-f)(L) x SU(N-f)(R) -> SU(N-f)(V). Second, we show that a QCD inequality implies a non-zero lower bound on the quark bilinear condensate.