Non-Abelian Axial-Vector Duality: a Geometric Description

TL;DR

This paper provides a geometric framework for understanding non-abelian axial-vector duality in sigma-models, highlighting the role of non-commutative conservation laws and quotient constructions.

Contribution

It introduces a geometric characterization of quasi axial-vector duality using bi-algebra methods and establishes criteria for duality via axial-vector procedures.

Findings

Sigma-models with non-abelian chiral currents obey non-commutative conservation laws

A criterion for sigma-models to admit duals using axial-vector procedures

A geometric interpretation of target space duality in non-abelian contexts

Abstract

We give a geometric characterization of the quasi axial-vector (Kiritsis-Obers) target space duality in the spirit of the bi-algebra (Klimcik-Severa) approach. We show that the sigma-models constructed by taking quotients have non-abelian chiral currents that obey "non-commutative conservation laws" and provide the criterion for a sigma-model to have a dual using the axial-vector procedure.