Poisson-Lie T-duality in Double Field Theory

‐Corrected Poisson‐Lie T‐Duality

“…[8][9][10] Hence, the objective of this letter is to construct leading order ′ -corrections to the PL T-duality transformation rules in a bosonic -model and to argue that they preserve conformal invariance. Key to this endeavour are three techniques: The formulation of PL symmetric target space geometries in the framework of Double Field Theory (DFT), [11] the ′ -corrected DFT flux formulation introduced by Marqués and Nuñez, [12] and finite generalised Green-Schwarz (gGS) transformations recently presented by Borsato, López, and Wulff. [10] PL T-duality and DFT: Directly at the level of the metric, Bfield, and dilaton, PL symmetric target spaces might look very complicated.…”

“…More precisely, the metric and the B-field can be unified in a generalised frame field [14] E A I on the generalised tangent space. It is governed by the frame algebra [11]…”

U-Dualities in Type II and M-Theory: A Covariant Approach

“…However, many fascinating applications of the DFT and ExFT formalisms have been left aside. Among these are non-abelian T-dualities in terms of Poisson-Lie transformations inside DFT [100,101]; generating supersymmetric vacua and consistent truncations of supergravity into lower dimensions [102][103][104] (for review see [105]); compactifications on non-geometric (Calabi-Yau) backgrounds and construction of cosmological models [54,55,106,107].…”

T-Duality and Doubling of the Isotropic Rigid Rotator

“…Many attempts have been done in the direction of generalizing the DFT description to Poisson-Lie T-duality, which is a generalization of the standard Abelian and non-Abelian concepts of T-dualities, see e.g. [50]. However, a manifest implementation of T-duality already at the level of world-sheet string action has not been yet clearly recovered, which would be of course even more interesting.…”

“…In this section we shortly review the mathematical setting of Drinfel'd doubles and Poisson-Lie T-duality, with particular focus on sl(2, C) as a double Lie algebra, which is needed in order to explore the relation between Drinfel'd doubles, Double Geometry and Generalized Geometry by introducing a new formulation of the IRR on sl(2, C) with manifest symmetry under duality. More information on these topics can be found in ref.s [1,36,46,49,50], which are going to be closely followed in this section.…”