Worldsheet boundary conditions in Poisson-Lie T-duality

Albertsson, Cecilia; Reid-Edwards, R.A.

doi:10.1088/1126-6708/2007/03/004

Cited by 16 publications

(21 citation statements)

References 34 publications

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“…Another example of a doubled geometry is Drinfel'd doubles, which are relevant in Poisson-Lie T-duality [38,39,40], a generalisation of T-duality to target spaces with nonabelian isometry, as well as to nonisometric target spaces. The study of D-branes in that framework encountered problems due to nonlocality issues [41], and we hope to resolve them by applying the present methodology.…”

Section: Discussionmentioning

confidence: 99%

D-branes and doubled geometry

Albertsson

Kimura

Reid-Edwards

2009

J. High Energy Phys.

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We define the open string version of the nonlinear sigma model on doubled geometry introduced by Hull and Reid-Edwards, and derive its boundary conditions. These conditions include the restriction of D-branes to maximally isotropic submanifolds as well as a compatibility condition with the Lie algebra structure on the doubled space. We demonstrate a systematic method to derive and classify D-branes from the boundary conditions, in terms of embeddings both in the doubled geometry and in the physical target space. We apply it to the doubled three-torus with constant H-flux and find D0-, D1-, and D2-branes, which we verify transform consistently under T-dualities mapping the system to f -, Q-and R-flux backgrounds.We also require the Neumann projector to be integrable, so that it locally defines the brane as a smooth submanifold of the target space,The projectors are moreover required to be orthogonal with respect to the doubled metric M IJ , 0 = Ξ I K M IJ Ξ

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Section: Discussionmentioning

confidence: 99%

D-branes and doubled geometry

Albertsson

Kimura

Reid-Edwards

2009

J. High Energy Phys.

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“…For more exotic notions of target space duality, e.g. non-Abelian [45,46] or Poisson-Lie [47,48], such an understanding is less refined (although see [49][50][51][52][53][54][55] and recent work in [56][57][58]) one reason being that the geometries concerned are not flat making it harder to identify the appropriate boundary conditions. Here however we will have access to an elegant description of D-brane boundary conditions in the λ-model whose interplay with duality can be readily studied.…”

Section: Jhep09(2018)015mentioning

confidence: 99%

D-branes in λ-deformations

Driezen

Sevrin

Thompson

2018

J. High Energ. Phys.

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We show that the geometric interpretation of D-branes in WZW models as twisted conjugacy classes persists in the λ-deformed theory. We obtain such configurations by demanding that a monodromy matrix constructed from the Lax connection of the λdeformed theory continues to produce conserved charges in the presence of boundaries. In this way the D-brane configurations obtained correspond to "integrable" boundary configurations. We illustrate this with examples based on SU(2) and SL(2, R), and comment on the relation of these D-branes to both non-Abelian T-duality and Poisson-Lie T-duality. We show that the D2 supported by D0 charge in the λ-deformed theory map, under analytic continuation together with Poisson-Lie T-duality, to D3 branes in the η-deformation of the principal chiral model.

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“…To obtain the non-zero Neumann-Neumann block of R one must use the condition (4.16). Then R takes, schematically, the following form [23]…”

Section: Worldsheet Boundary Conditions Under the Poisson-lie T-dualitymentioning

confidence: 99%

“…The goal is then to find the restrictions on this ansatz arising from varying the action (2.8). The most general local boundary condition may be expressed as [23] ∂…”

Section: Worldsheet Boundary Conditions Under the Poisson-lie T-dualitymentioning

confidence: 99%

Poisson Lie symmetry and D-branes in WZW model on the Heisenberg Lie group H 4

Eghbali

Rezaei-Aghdam

2015

Nuclear Physics B

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We show that the WZW model on the Heisenberg Lie group H 4 has Poisson-Lie symmetry only when the dual Lie group is A 2 ⊕ 2A 1 . In this way, we construct the mutual T-dual sigma models on Drinfel'd double generated by the Heisenberg Lie group H 4 and its dual pair, A 2 ⊕ 2A 1 , as the target space in such a way that the original model is the same as the H 4 WZW model. Furthermore, we show that the dual model is conformal up to two-loop order. Finally, we discuss D-branes and the worldsheet boundary conditions defined by a gluing matrix on the H 4 WZW model. Using the duality map obtained from the canonical transformation description of the Poisson-Lie T-duality transformations for the gluing matrix which locally defines the properties of the D-brane, we find two different cases of the gluing matrices for the WZW model based on the Heisenberg Lie group H 4 and its dual model.

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Worldsheet boundary conditions in Poisson-Lie T-duality

Cited by 16 publications

References 34 publications

D-branes and doubled geometry

D-branes and doubled geometry

D-branes in λ-deformations

Poisson Lie symmetry and D-branes in WZW model on the Heisenberg Lie group H 4

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