Abstract
AbstractIn this note we study exceptional algebroids, focusing on their relation to type IIB superstring theory. We show that a IIB‐exact exceptional algebroid (corresponding to the group , for ) locally has a standard form given by the exceptional tangent bundle. We derive possible twists, given by a flat ‐connection, a covariantly closed pair of 3‐forms, and a 5‐form, and comment on their physical interpretation. Using this analysis we reduce the search for Leibniz parallelisable spaces, and hence maximally supersymmetric consistent truncations, to a simple algebraic problem. We show that the exceptional algebroid perspective also gives a simple description of Poisson–Lie U‐duality without spectators and hence of generalised Yang–Baxter deformations.
Highlights
Defining the notion of exact elgebroids leads to two classes, related to the elevendimensional and type IIB supergravity
We gave an algebroid definition of. It has been known for some time that various classes of alge- the general notion of Poisson–Lie U-duality, extending the conbroids play an important role in string and M-theory
Supposing E is a IIB-exact2 pre-elgebroid, we note that locally there exists a vector bundle isomorphism (6), which preserves the anchors and the G-structure. This follows from the facts that both (S ⊗ T∗M) ⊕ ∧3 T∗M ⊕ (S ⊗ ∧5 T∗M) and Ker ρ are type IIB co
Summary
We recall the algebraic data one needs to define an elgebroid following [9]. Www.advancedsciencenews.com www.fp-journal.org group En(n), together with a pair of its representations E and N, from the following table. These groups (apart from R) can be seen as split real forms of complex semisimple Lie algebras. (u ⊗ v)N for the image of u ⊗ v under the former map or (ξ ⊗ n)E for E∗ ⊗ N → E, a partial dual of the latter map) Using these maps we can define the notions of Lagrangian and co-Lagrangian subspaces. V ⊂ E is co-Lagrangian if (V◦ ⊗ V◦)N∗ = 0 and if V has no proper subspace with the same property.
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