Implications of Certain Algebraic Aspects of Dual Resonance Models

Abstract

Certain algebraic aspects present in the dual resonance models led Susskind and Frye to the construction of $n$-point pion amplitudes in the tree-graph approximation which are a sum of terms, each one coming from a distinct permutation and satisfying the Adler's condition separately. It was also shown that this line of reasoning picks up a definite form of chiral symmetry breaking (in $\mathrm{SU}2\ensuremath{\bigotimes}\mathrm{SU}2$). In this work we show that the extension to the pseudoscalar multiplet forces one to include the whole nonet. The resulting amplitudes coincide with those obtained from an $U(3)\ensuremath{\bigotimes}U(3)$ model with the chiral symmetry broken in a way that preserves the complete nonet degeneracy.