Algebraic Aspects of Pionic Duality Diagrams

Certain algebraic aspects are abstracted from the duality principle and are incorporated in a simple model of pion $n$-point functions. An algorithm for constructing the $n$-point function in the tree-graph approximation is based on the duality assumption and the Adler condition which states that the amplitudes vanishes if any pion four-momentum vanishes, all others remaining on shell. The resulting amplitudes satisfy the constraints of current algebra and partial conservation of axial-vector current for $n=4, 6, \mathrm{and} 8$, and (we conjecture) for all $n$. In addition, duality specifies a definite form for chiral symmetry breaking.