CANONICAL NONABELIAN DUAL TRANSFORMATIONS IN SUPERSYMMETRIC FIELD THEORIES

TL;DR

This paper introduces a generating functional for a nonabelian dual transformation in supersymmetric field theories, mapping the supersymmetric chiral O(4) sigma-model to its dual with specific local and nonlocal field transformations.

Contribution

It provides the first explicit construction of a generating functional for nonabelian duality in supersymmetric models, detailing the classical and quantum mappings between the theories.

Findings

Classical phase space mapping with nonlocal bosonic and local fermionic transformations.

Dual currents mix bosonic and fermionic components, forming a symphysis.

Quantum wavefunction transformation given by the exponential of the generating functional.

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 $T=\exp(iF)$.