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 $T=\exp (iF)$.

5 pages, Revtex

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• Killing-Yano Supersymmetry in String Theory
• Geometry and Duality in Supersymmetric sigma-Models
• Poisson-Lie T-duality and Complex Geometry in N=2 superconformal WZNW models
• First Order Actions and Duality
• A Novel Symmetry in Sigma Models
• S-duality and Canonical Transformations in String Theory
• Supersymmetric Quantum Corrections and Poisson-Lie T-Duality