Doubling, T-Duality and Generalized Geometry: a Simple Model

TL;DR

This paper explores a simple mechanical model, the isotropic rigid rotator, within the framework of Generalized Geometry and Double Field Theory, revealing how dualities and geometric structures can be understood in a unified setting.

Contribution

It introduces a generalized action on the Drinfel'd double of SU(2), linking the rotator model to generalized geometry and duality concepts, with a novel geometric interpretation.

Findings

The model's generalized action reduces to original or dual actions with constraints.

The geometric structures are interpretable via Generalized Geometry.

The approach connects simple mechanical systems to advanced duality frameworks.

Abstract

A simple mechanical system, the three-dimensional isotropic rigid rotator, is here investigated as a 0+1 field theory, aiming at further investigating the relation between Generalized/Double Geometry on the one hand and Doubled World-Sheet Formalism/Double Field Theory, on the other hand. The model is defined over the group manifold of SU(2) and a dual model is introduced having the Poisson-Lie dual of SU(2) as configuration space. A generalized action with configuration space SL(2,C), i.e. the Drinfel'd double of the group SU(2), is then defined: it reduces to the original action of the rotator or to its dual, once constraints are implemented. The new action contains twice as many variables as the original. Moreover, its geometric structures can be understood in terms of Generalized Geometry. keywords: Generalized Geometry, Double Field Theory, T-Duality, Poisson-Lie symmetry.