On the Non-Abelian U-Duality of 11D Backgrounds

Musaev, Edvard T.

doi:10.3390/universe8050276

Cited by 10 publications

(3 citation statements)

References 62 publications

(114 reference statements)

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“…Finally, we should add that very significant work on U-duality extensions of Poisson-Lie T-duality and its generalizations has appeared recently [111][112][113][114][115][116][117]. These would undoubtedly have natural descriptions in supersymmetric extensions of U-dual formulations, of the type explored e.g.…”

Section: Jhep12(2023)052 7 Discussionmentioning

confidence: 97%

Generalized dualities and supergroups

Butter,

Hassler,

Pope

et al. 2023

J. High Energ. Phys.

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Using a recently developed formulation of double field theory in superspace, the graviton, B-field, gravitini, dilatini, and Ramond-Ramond bispinor are encoded in a single generalized supervielbein. Duality transformations are encoded as orthosymplectic transformations, extending the bosonic O(D, D) duality group, and these act on all constituents of the supervielbein in an easily computable way. We first review conventional non-abelian T-duality in the Green-Schwarz superstring and describe the dual geometries in the language of double superspace. Since dualities are related to super-Killing vectors, this includes as special cases both abelian and non-abelian fermionic T-duality.We then extend this approach to include Poisson-Lie T-duality and its generalizations, including the generalized coset construction recently discussed in [arXiv:1912.11036]. As an application, we construct the supergeometries associated with the integrable λ and η deformations of the AdS5 × S5 superstring. The deformation parameters λ and η are identified with the possible one-parameter embeddings of the supergravity frame within the doubled supergeometry. In this framework, the Ramond-Ramond bispinors are directly computable purely from the algebraic data of the supergroup.

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Section: Jhep12(2023)052 7 Discussionmentioning

confidence: 97%

Generalized dualities and supergroups

Butter,

Hassler,

Pope

et al. 2023

J. High Energ. Phys.

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“…What is dubbed Q-flux here has recently been of considerable interest in the context of non-abelian U-duality, exceptional Drinfeld algebras and the construction of new uplifts to lower dimensional to 11-dimensional supergravity recently [37,[70][71][72][73][74][75][76][77][78][79][80][81][82][83]. The trace-free resp.…”

Section: Jhep01(2024)028mentioning

confidence: 99%

On exceptional QP-manifolds

Osten

2024

J. High Energ. Phys.

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The connection between two recent descriptions of tensor hierarchies — namely, infinity-enhanced Leibniz algebroids, given by Bonezzi & Hohm and Lavau & Palmkvist, and the p-brane QP-manifolds constructed by Arvanitakis — is made precise. This is done by presenting a duality-covariant version of latter.The construction is based on the QP-manifold T⋆[n]T[1]M × ℋ[n], where M corresponds to the internal manifold of a supergravity compactification and ℋ[n] to a degree-shifted version of the infinity-enhanced Leibniz algebroid. Imposing that the canonical Q-structure on T⋆[n]T[1]M is the derivative operator on ℋ leads to a set of constraints. Solutions to these constraints correspond to $$ \frac{1}{2} $$ 1 2 -BPS p-branes, suggesting that this is a new incarnation of a brane scan. Reduction w.r.t. to these constraints reproduces the known p-brane QP-manifolds. This is shown explicitly for the SL(3)×SL(2)- and SL(5)-theories.Furthermore, this setting is used to speculate about exceptional ‘extended spaces’ and QP-manifolds associated to Leibniz algebras. A proposal is made to realise differential graded manifolds associated to Leibniz algebras as non-Poisson subspaces (i.e. not Poisson reductions) of QP-manifolds similar to the above. Two examples for this proposal are discussed: generalised fluxes (including the dilaton flux) of O(d, d) and the 3-bracket flux for the SL(5)-theory.

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“…More concretely the multiplication table can be represented in the following form the rest of generators do not form an algebra. However, an analogue of such swapping has been suggested in [138] based on outer automorphisms of e d , that allowed to generate several examples of non-abelian U-dual backgrounds in [110].…”

Section: Nambu-lie U-dualitymentioning

confidence: 99%

Integrability structures in string theory

Gubarev¹,

Musaev²

2023

Preprint

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This review is a collection of various methods and observations relevant to structures in three-dimensional systems similar to those responsible for integrability of two-dimensional systems. Particular focus is given to Nambu structures and loop variables naturally appearing in membrane dynamics. While reviewing each topic in more details we emphasize connections between them and speculate on possible relations to membrane integrability.

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On the Non-Abelian U-Duality of 11D Backgrounds

Cited by 10 publications

References 62 publications

Generalized dualities and supergroups

Generalized dualities and supergroups

On exceptional QP-manifolds

Integrability structures in string theory

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