Metric Algebroid and Poisson-Lie T-duality in DFT

TL;DR

This paper develops a metric algebroid framework for Double Field Theory (DFT) that does not rely on the section condition, enabling a unified treatment of gauge invariance, duality, and Poisson-Lie T-duality.

Contribution

It introduces a section condition-independent action for DFT based on metric algebroids, linking gauge invariance, duality, and the pre-Bianchi identity, with applications to Poisson-Lie T-duality.

Findings

Derived a general DFT action without the section condition.

Established the role of the pre-Bianchi identity in gauge invariance.

Applied the framework to Poisson-Lie T-duality on group manifolds.

Abstract

In this article we investigate the gauge invariance and duality properties of DFT based on a metric algebroid formulation given previously in [1]. The derivation of the general action given in this paper does not employ the section condition. Instead, the action is determined by requiring a pre-Bianchi identity on the structure functions of the metric algebroid and also for the dilaton flux. The pre-Bianchi identity is also a sufficient condition for a generalized Lichnerowicz formula to hold. The reduction to the D-dimensional space is achieved by a dimensional reduction of the fluctuations. The result contains the theory on the group manifold, or the theory extending to the GSE, depending on the chosen background. As an explicit example we apply our formulation to the Poisson-Lie T-duality in the effective theory on a group manifold. It is formulated as a 2D-dimensional diffeomorphism including the fluctuations.