Chiral Symmetry Breaking and Quark Bilinear Condensate in Large N QCD

Abstract

We discuss spontaneous chiral symmetry breaking and quark bilinear condensate in large $N_c$ QCD. It has been known that the existence of ${\eta }^{\prime }$ meson is implied in large $N_c$ QCD as pointed out by Witten and Veneziano. First, we show that the existence of ${\eta }^{\prime }$ and Ward-Takahashi identities imply the existence of the Nambu-Goldstone bosons from chiral symmetry breaking $SU(N_f{)}_L\times SU(N_f{)}_R\to SU(N_f{)}_V$. Second, we show that a QCD inequality implies a nonzero lower bound on the quark bilinear condensate.

Comments: 8 pages, v2: published version