Thomas Curtright — Page 3

arXiv1996

Geometry and Duality in Supersymmetric sigma-Models

The Supersymmetric Dual Sigma Model (SDSM) is a local field theory introduced to be nonlocally equivalent to the Supersymmetric Chiral nonlinear sigma-Model (SCM), this dual equivalence being proven by explicit canonical transformation in tangent space. This model is here reconstructed in superspace and identified as a chiral-entwined supersymmetrization of the Dual Sigma Model (DSM). This analysis sheds light on the Boson-Fermion Symphysis of the dual transition, and on the new geometry of the DSM.

hep-th↗

arXiv1995

CANONICAL NONABELIAN DUAL TRANSFORMATIONS IN SUPERSYMMETRIC FIELD THEORIES

A generating functional $F$ is found for a canonical nonabelian 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 {\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 $T=\exp(iF)$.

hep-th↗