A generating functional F is found for a canonical non-Abelian dual transformation which maps the supersymmetric chiral O(4) σ model to an equivalent supersymmetric extension of the dual σ 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 symphysis of purely bosonic and fermion bilinear currents of the dual theory. The corresponding transformation functional T which relates wave functions in the two quantum theories is argued to be exactly given by T=exp(iF).
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)