Dual-Pion Model Satisfying Current-Algebra Constraints

The dual-pion model, previously constructed with ${m_{\pi }}^2=-\frac{1}{2}$ and ${m_{\rho }}^2=0\mathrm{}$, is generalized to arbitrary pion mass while maintaining the relation ${m_{\rho }}^2={m_{\pi }}^2+\frac{1}{2}$. As in the conventional dual-resonance model, the price for doing this is the introduction of ghosts. In the special case $m_{\pi }=0\mathrm{}$, the $N$-pion amplitudes are shown to possess Adler zeros, and, as a consequence, to satisfy the constraints that current algebra imposes on on-mass-shell hadron amplitudes. The axial charges are explicitly constructed and shown to close with the isospin to form the algebra of SU(2) × SU(2). This model should provide a useful theoretical laboratory for studying the consequences of combining duality and current-algebra constraints. The construction of currents is a challenging problem.