Non--Abelian Duality, Parafermions and Supersymmetry

TL;DR

This paper explores how non-Abelian duality affects supersymmetry, revealing non-local realizations involving Wilson lines and parafermions, and establishes equivalences between WZW models and their duals.

Contribution

It demonstrates the non-local realization of extended supersymmetry after non-Abelian duality and establishes the equivalence of WZW models with their duals.

Findings

Extended supersymmetry becomes non-local after duality.

Non-Abelian parafermions naturally arise in dual models.

WZW models are canonically equivalent to their non-Abelian duals.

Abstract

Non--Abelian duality in relation to supersymmetry is examined. When the action of the isometry group on the complex structures is non--trivial, extended supersymmetry is realized non--locally after duality, using path ordered Wilson lines. Prototype examples considered in detail are, hyper--Kahler metrics with SO(3) isometry and supersymmetric WZW models. For the latter, the natural objects in the non--local realizations of supersymmetry arising after duality are the classical non--Abelian parafermions. The canonical equivalence of WZW models and their non--Abelian duals with respect to a vector subgroup is also established.