Structure of Massless Composite Fermions and Large N Limit

Abstract

Composite fermions with two flavor chiral symmetry, which is massless by satisfying the anomaly conditions; are examined in the large N limit of underlying SU(N) gauge theory. In the case when the fermion F is an N ·body composite of massless chiral fermionic constituent I belonging to N -plet of SU(N), neither the planar dominance nor the OZI suppression holds in the large N limit. In contrast, when one fermionic constituent I and one bosonic constituent <p of N -plet are bound into the massless F = lip, both the planar dominance and the OZI suppression are possible to be guaranteed. As an applica­ tion, some results in the large N limit when the latter type structure is assumed for massless composite quarks and leptons with the Pati-Salam index are also given. § 1. Introduction and summary The realization mode of chiral flavor symmetry with underlying SU(N) gauge theory, which is of dynamical character, is one of crucial problems of possible ~omposite quarks and leptons. It is well known that in the hadronic world the chiral symmetry is realized in the Nambu-Goldstone (broken) mode with massless isotriplet pions (Nambu­ Goldstone bosons) and massive isodoublet nucleons in the two flavor case. On the contrary, the chiral realization is expected to be in the Wigner (unbroken) mode for possible composite quarks and leptons, as their masses are negligibly small compared with the mass scale of underlying gauge theory inferred from their inverse sizes. On the other hand, the 1/ N expansion is known to be a fruitful approximation to SU(N) gauge theory. I) Several hadronic aspects such as the planar dominance and the OZI (Okubo-Zweig-Iizuka) suppression have no other explanations than in the large N limit. Note, however, that the explanation has been complete only in the meson sector. Generalization to the baryon sector is impossible without further dynamical assumptions as seen in §2. The problem we examine in this article is the structure of massless composite fer­ mions, denoted by F, in the large N limit by assuming the Wigner realization mode of chiral flavor symmetry. The masslessness requirement is met by t'Hooft's anomaly matching conditions 2 ) for the triangle diagram coupled to three flavor currents. To have simple solutions to the conditions, we restrict ourselves to the case of two flavors. Namely, we assume the chiral flavor symmetry