Chiral Symmetry Breaking and Quark Bilinear Condensate in Large N QCD

TL;DR

This paper demonstrates that in large N_c QCD, chiral symmetry breaking leads to Nambu-Goldstone bosons and a nonzero quark condensate, supported by Ward-Takahashi identities and QCD inequalities.

Contribution

It establishes the connection between the existence of the $ extit{ extbf{eta}}'$ meson, Ward-Takahashi identities, and the nonzero quark condensate in large N_c QCD, providing a theoretical foundation.

Findings

Existence of $ extit{ extbf{eta}}'$ meson implied in large N_c QCD.

Ward-Takahashi identities lead to Nambu-Goldstone bosons from chiral symmetry breaking.

QCD inequality sets a nonzero lower bound on the quark bilinear condensate.

Abstract

We discuss spontaneous chiral symmetry breaking and quark bilinear condensate in large $N_c$ QCD. It has been known that the existence of $\eta'$ meson is implied in large $N_c$ QCD as pointed out by Witten and Veneziano. First, we show that the existence of $\eta'$ 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.