Doubled aspects of generalised dualities and integrable deformations

Demulder, Saskia; Haßler, Falk; Thompson, Daniel C.

doi:10.1007/jhep02(2019)189

Cited by 81 publications

(127 citation statements)

References 156 publications

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“…In essence, Poisson-Lie models, i.e. models where Poisson-Lie duality can act, arise as a generalised Scherk-Schwarz reduction [26,27] in which all non-trivial coordinate dependance is encoded in a twist matrix, or generalised frame field, E A I as was first shown in [28] and developed in [29]. Through the Courant bracket, the generalised frame fields of [28] realise the algebra of a Drinfeld double and depend crucially on the properties of the Poisson-Lie bi-vector upon which Poisson-Lie duality relies.…”

Section: Introductionmentioning

confidence: 99%

Poisson-Lie U-duality in exceptional field theory

Malek

Thompson

2020

J. High Energ. Phys.

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Poisson-Lie duality provides an algebraic extension of conventional Abelian and non-Abelian target space dualities of string theory and has seen recent applications in constructing quantum group deformations of holography. Here we demonstrate a natural upgrading of Poisson-Lie to the context of M-theory using the tools of exceptional field theory. In particular, we propose how the underlying idea of a Drinfeld double can be generalised to an algebra we call an exceptional Drinfeld algebra. These admit a notion of "maximally isotropic subalgebras" and we show how to define a generalised Scherk-Schwarz truncation on the associated group manifold to such a subalgebra. This allows us to define a notion of Poisson-Lie U-duality. Moreover, the closure conditions of the exceptional Drinfeld algebra define natural analogues of the cocycle and co-Jacobi conditions arising in Drinfeld double. We show that upon making a further coboundary restriction to the cocycle that an M-theoretic extension of Yang-Baxter deformations arise. We remark on the application of this construction as a solution-generating technique within supergravity.

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Section: Introductionmentioning

confidence: 99%

Poisson-Lie U-duality in exceptional field theory

Malek

Thompson

2020

J. High Energ. Phys.

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“…A new formulation of DFT on group manifolds (called DFT WZW ) has been developed in [20][21][22], and in the recent works [23,24], the PL T -duality has been studied in the framework of DFT WZW . In more recent papers [7,25], the non-Abelian T -duality and the PL T -duality have been discussed by using another approach, called the gauged DFT [26][27][28][29][30][31] (see also [32,33] for recent discussion on the Drinfel'd double and related aspects in DFT).…”

Section: Introductionmentioning

confidence: 99%

U -duality extension of Drinfel’d double

Sakatani

2020

Progress of Theoretical and Experimental Physics

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Abstract A family of algebras $\mathcal{E}_n$ that extends the Lie algebra of the Drinfel’d double is proposed. This allows us to systematically construct the generalized frame fields $E_A{}^I$ which realize the proposed algebra by means of the generalized Lie derivative, i.e., $\hat{\pounds}_{E_A}E_B{}^I =-\mathcal{F}_{AB}{}^C\,E_C{}^I$. By construction, the generalized frame fields include a twist by a Nambu–Poisson tensor. A possible application to the non-Abelian extension of $U$-duality and a generalization of the Yang–Baxter deformation are also discussed.

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“…Here x A denotes the push forward x A = π * E −1 T A where π projects from P to M (π : P → M ). If we additionally impose the constraint (3.10) the second term of ϕ A vanishes and the frame field is equivalent to the one discussed by [79] in the context of DFT WZW . Let us finally rewrite the frame algebra (3.33) that we proved above in the language of DFT.…”

Section: Double Field Theory On Group Manifoldsmentioning

confidence: 99%

Para-Hermitian geometries for Poisson-Lie symmetric σ-models

Haßler

Lüst

Rudolph

2019

J. High Energ. Phys.

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The doubled target space of the fundamental closed string is identified with its phase space and described by an almost para-Hermitian geometry. We explore this setup in the context of group manifolds which admit a maximally isotropic subgroup. This leads to a formulation of the Poisson-Lie σ-model and Poisson-Lie T-duality in terms of para-Hermitian geometry. The emphasis is put on so called half-integrable setups where only one of the Lagrangian subspaces of the doubled space has to be integrable. Using the dressing coset construction in Poisson-Lie T-duality, we extend our construction to more general coset spaces. This allows to explicitly obtain a huge class of para-Hermitian geometries. Each of them is automatically equipped which a generalized frame field, required for consistent generalized Scherk-Schwarz reductions. As examples we present integrable λ-and η-deformations on the three-and two-sphere.

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Doubled aspects of generalised dualities and integrable deformations

Cited by 81 publications

References 156 publications

Poisson-Lie U-duality in exceptional field theory

Poisson-Lie U-duality in exceptional field theory

U -duality extension of Drinfel’d double

Para-Hermitian geometries for Poisson-Lie symmetric σ-models

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