Metric Algebroid and Poisson-Lie T-duality in DFT

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.