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

Abstract

We discuss spontaneous chiral symmetry breaking and the quark bilinear condensate in large-Nc quantum chromodynamics (QCD). It is known that the existence of the η′ meson is implied in large-Nc QCD, as pointed out by Witten[27] and Veneziano[28]. First, we show that the existence of η′ and the Ward-Takahashi identities implies the existence of Nambu-Goldstone bosons from chiral symmetry breaking SU(Nf)L × SU(Nf)R → SU(Nf)V. Second, we show that a QCD inequality implies a non-zero lower bound on the quark bilinear condensate.