Non-Abelian Duality and Canonical Transformations

TL;DR

Addresses non-abelian target-space duality for sigma-models via a canonical-transformation framework. Introduces a type I generating functional that enacts the duality for a left G-action and derives the dual Hamiltonian with structure-constant interactions, illustrating with the SU(2) case. Discusses extensions to subgroups and WZW models, and argues for potential exactness of the duality at the quantum level under eigenfunction matching, while noting possible quantum corrections. This work provides a concrete, path-integral compatible route to non-abelian duality and sets the stage for higher-genus generalizations and deeper current-transform relation analyses.

Abstract

We construct explicit canonical transformations producing non-abelian duals in principal chiral models with arbitrary group G. Some comments concerning the extension to more general $σ$-models, like WZW models, are given.