CANONICAL NONABELIAN DUAL TRANSFORMATIONS IN SUPERSYMMETRIC FIELD THEORIES

Abstract

A generating functional $F$ is found for a canonical nonabelian dual transformation which maps the supersymmetric chiral O(4) $\sigma$-model to an equivalent supersymmetric extension of the dual $\sigma$-model. This $F$ produces a mapping between the classical phase spaces of the two theories in which the bosonic (coordinate) fields transform nonlocally, the fermions undergo a local tangent space chiral rotation, and all currents (fermionic and bosonic) mix locally. Purely bosonic curvature-free currents of the chiral model become a {\em symphysis} of purely bosonic and fermion bilinear currents of the dual theory. The corresponding transformation functional $T$ which relates wavefunctions in the two quantum theories is argued to be {\em exactly} given by $T=\exp(iF)$.