Non-Abelian Momentum-Winding Exchange

TL;DR

This paper introduces a non-Abelian generalization of the Abelian T-duality, relating sigma-models on cosets of a Drinfeld double and extending the concept of momentum-winding exchange beyond Abelian cases.

Contribution

It develops a non-Abelian T-duality framework that connects sigma-models on cosets of Drinfeld doubles, generalizing the Abelian momentum-winding exchange.

Findings

Establishes a non-Abelian T-duality relation for sigma-models.

Identifies the fundamental group of the Drinfeld double as the non-Abelian analogue of the Abelian lattice.

Provides a mathematical description linking non-Abelian duality to Drinfeld doubles.

Abstract

A non-Abelian analogue of the Abelian T-duality momentum-winding exchange is described. The non-Abelian T-duality relates $\sigma$-models living on the cosets of a Drinfeld double with respect to its isotropic subgroups. The role of the Abelian momentum-winding lattice is in general played by the fundamental group of the Drinfeld double.