Tri-vector deformations in d = 11 supergravity

Bakhmatov, Ilya; Deger, Nihat Sadik; Musaev, Edvard T.; Colgáin, Eoin Ó; Sheikh-Jabbari, M. M.

doi:10.1007/jhep08(2019)126

Cited by 35 publications

(56 citation statements)

References 116 publications

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“…Recently, an 11D extension of this YB deformation has been studied in [80]. There, the YB deformation is generalized to the Ω-deformation Ω i 1 i 2 i 3 → Ω ′i 1 i 2 i 3 = Ω i 1 i 2 i 3 + ρ i 1 i 2 i 3 associated with a tri-Killing vector…”

Section: Summary and Discussionmentioning

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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Section: Summary and Discussionmentioning

confidence: 99%

U -duality extension of Drinfel’d double

Sakatani

2020

Progress of Theoretical and Experimental Physics

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“…An obvious question is then if these generalised Poisson-Lie type T-dualities can be extended to generalised notions of U-duality. Though some partial descriptions have been recently suggested in the literature [33], thus far an algebraically robust description has been lacking. It is this that we address in the current article in the context of exceptional field theory (ExFT)/exceptional generalised geometry [34][35][36][37][38][39][40], the M-theoretic analogues to Double Field Theory/generalised geometry.…”

Section: Previous Attempts To Understand Poisson-lie T-duality and Nomentioning

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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“…This might also provide a method to carry out some of the generalisations mentioned above. Further, it would be interesting to compare this construction with that of [60,61] where the trivector is viewed as a deformation of a pre-existing geometry.…”

Section: Jhep09(2020)151mentioning

confidence: 99%

Exploring exceptional Drinfeld geometries

Blair

Thompson

Zhidkova

2020

J. High Energ. Phys.

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We explore geometries that give rise to a novel algebraic structure, the Exceptional Drinfeld Algebra, which has recently been proposed as an approach to study generalised U-dualities, similar to the non-Abelian and Poisson-Lie generalisations of T-duality. This algebra is generically not a Lie algebra but a Leibniz algebra, and can be realised in exceptional generalised geometry or exceptional field theory through a set of frame fields giving a generalised parallelisation. We provide examples including “three-algebra geometries”, which encode the structure constants for three-algebras and in some cases give novel uplifts for CSO(p, q, r) gaugings of seven-dimensional maximal supergravity. We also discuss the M-theoretic embedding of both non-Abelian and Poisson-Lie T-duality.

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Tri-vector deformations in d = 11 supergravity

Cited by 35 publications

References 116 publications

U -duality extension of Drinfel’d double

U -duality extension of Drinfel’d double

Poisson-Lie U-duality in exceptional field theory

Exploring exceptional Drinfeld geometries

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