Poisson-Lie T-duality: Open Strings and D-branes

Abstract

Global issues of the Poisson-Lie T-duality are addressed. It is shown that oriented open strings propagating on a group manifold $G$ are dual to $D$-brane - anti-$D$-brane pairs propagating on the dual group manifold $\ti G$. The $D$-branes coincide with the symplectic leaves of the standard Poisson structure induced on the dual group $\ti G$ by the dressing action of the group $G$. T-duality maps the momentum of the open string into the mutual distance of the $D$-branes in the pair. The whole picture is then extended to the full modular space $M(D)$ of the Poisson-Lie equivalent $\si$-models which is the space of all Manin triples of a given Drinfeld double.T-duality rotates the zero modes of pairs of $D$-branes living on targets belonging to $M(D)$. In this more general case the $D$-branes are preimages of symplectic leaves in certain Poisson homogeneous spaces of their targets and, as such, they are either all even or all odd dimensional.

15 pages, LaTeX (references added)

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Cited by in corpus (32)

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• Generalised fluxes, Yang-Baxter deformations and the O(d,d) structure of non-abelian T-duality
• Aspects of T-duality in Open Strings
• Strings, Branes and Extra Dimensions
• Duality in String Theory
• Dressing cosets and multi-parametric integrable deformations
• Target Space Duality I: General Theory
• Curvature from quantum deformations
• Target Space Duality II: Applications
• On current algebras, generalised fluxes and non-geometry
• Non-Abelian Duality for Open Strings
• Target Space Pseudoduality Between Dual Symmetric Spaces
• T-Duality for Coset Models
• Worldsheet boundary conditions in Poisson-Lie T-duality
• D-branes on Group Manifolds and Deformation Quantization
• D-branes in $\lambda$-deformations
• On the Poisson-Lie T-plurality of boundary conditions
• On modular spaces of semisimple Drinfeld doubles
• Open-string T-duality and applications to non-geometric backgrounds
• Solution of the equations of motion for a super non-Abelian sigma model in curved background by the super Poisson-Lie T-duality
• Poisson-Lie T-duality and (1,1) supersymmetry
• Non-Abelian T-duality for open strings
• Poisson-Lie T-duality defects and target space fusion
• D-branes (or not) in the non-Abelian T-dual of the SU(2) WZW model
• Open string T-duality in a weakly curved background
• D-branes in the Euclidean $Ad{S}_3$ and T-duality
• Beyond Noether: A Covariant Study of Poisson-Lie Symmetries in Low Dimensional Field Theory
• Integrable branes in generalized $\lambda$-deformations