Type II DFT solutions from Poisson-Lie T-duality/plurality

Abstract

String theory has the T-duality symmetry when the target space has Abelian isometries. A generalization of the T-duality, where the isometry group is non-Abelian, is known as the non-Abelian T-duality, which works well as a solution-generating technique in supergravity. In this paper, we describe the non-Abelian T-duality as a kind of O(D,D) transformation when the isometry group acts without isotropy. We then provide a duality transformation rule for the Ramond-Ramond fields by using the technique of double field theory (DFT). We also study a more general class of solution-generating technique, the Poisson-Lie (PL) T-duality or T-plurality. We describe the PL T-plurality as an O(n,n) transformation and clearly show the covariance of the DFT equations of motion by using the gauged DFT. We further discuss the PL T-plurality with spectator fields, and study an application to the AdS${}_5\times$S${}^5$ solution. The dilaton puzzle known in the context of the PL T-plurality is resolved with the help of DFT.

80 pages + references; v2: clarifications added, appendix B added which shows the covariance under the PL T-plurality with spectators; v3: typos corrected; v4: references added

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Cited by in corpus (30)

• The Geometry, Branes and Applications of Exceptional Field Theory
• U-duality extension of Drinfel'd double
• E${}_{6(6)}$ Exceptional Drinfel'd Algebras
• Quantum correction to generalized T-dualities
• Remarks on the non-Riemannian sector in Double Field Theory
• String Theory and non-Riemannian Geometry
• Generalized Dualities and Higher Derivatives
• Non-Abelian U-duality for membrane
• Exploring Exceptional Drinfeld Geometries
• Yang-Baxter Deformation as an O(d,d) Transformation
• Non-abelian U-duality at work
• On non-abelian U-duality of 11D backgrounds
• Consistent Truncations and Dualities
• Born Sigma-Models for Para-Hermitian Manifolds and Generalized T-Duality
• Global Aspects of Doubled Geometry and Pre-rackoid
• All maximal gauged supergravities with uplift
• Generalized Dualities and Supergroups
• More on Doubled Aspects of Algebroids in Double Field Theory
• The Magic Renormalisability of Affine Gaudin Models
• Jacobi-Lie T-plurality
• Poisson-Lie transformations and Generalized Supergravity Equations
• Compatibility of Poisson--Lie transformations with symmetries of Generalized Supergravity Equations
• Metric Algebroid and Poisson-Lie T-duality in DFT
• T-folds as Poisson-Lie plurals
• $Ad{S}_3\times S^3$ Background from Poisson-Lie T-Duality
• Jacobi-Lie Models and Supergravity Equations
• Extended Doubled Structures of Algebroids for Gauged Double Field Theory
• Plane-parallel waves as Jacobi-Lie models
• Double Field Theory for Generalized $\lambda$-deformation
• On spectator dependence of Jacobi-Lie T-plurality