Exceptional algebroids and type IIB superstrings

Abstract

In 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 $E_{n(n)}\times {\mathbb{R}}^{+}$, for $n\le 6$) locally has a standard form given by the exceptional tangent bundle. We derive possible twists, given by a flat $\mathfrak{gl}(2,\mathbb{R})$-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.

12 pages

References in corpus (33)

• Dual Non-Abelian Duality and the Drinfeld Double
• Generalised Geometry for M-Theory
• The gauge algebra of double field theory and Courant brackets
• Supergravity as Generalised Geometry I: Type II Theories
• M-theory, exceptional generalised geometry and superpotentials
• Exceptional Field Theory I: $E_{6(6)}$ covariant Form of M-Theory and Type IIB
• The gauge structure of generalised diffeomorphisms
• Lectures on Gauged Supergravity and Flux Compactifications
• Consistent Kaluza-Klein Truncations via Exceptional Field Theory
• Supersymmetric AdS_5 Solutions of Type IIB Supergravity
• Gauged Supergravities, Tensor Hierarchies, and M-Theory
• M-theory and Type IIB from a Duality Manifest Action
• Leibniz algebroids, twistings and exceptional generalized geometry
• Half-maximal supersymmetry from exceptional field theory
• The exceptional story of massive IIA supergravity
• Exceptional generalised geometry for massive IIA and consistent reductions
• Systematics of consistent truncations from generalised geometry
• U-duality extension of Drinfel'd double
• Poisson-Lie U-duality in Exceptional Field Theory
• Generalised Scherk-Schwarz reductions from gauged supergravity
• Letters to Alan Weinstein about Courant algebroids
• E${}_{6(6)}$ Exceptional Drinfel'd Algebras
• Poisson-Lie T-duality and Courant algebroids
• Tri-vector deformations in $d=11$ supergravity
• Double Field Theory at SL(2) angles
• Exceptional Calabi--Yau spaces: the geometry of $\mathcal{N}=2$ backgrounds with flux
• Non-abelian tri-vector deformations in d=11 supergravity
• Poisson-Lie T-duality as a boundary phenomenon of Chern-Simons theory
• Exploring Exceptional Drinfeld Geometries
• G-algebroids: a unified framework for exceptional and generalised geometry, and Poisson-Lie duality
• Generalized Parallelizable Spaces from Exceptional Field Theory
• Non-abelian Gerbes and Enhanced Leibniz Algebras
• Enhanced Leibniz Algebras: Structure Theorem and Induced Lie 2-Algebra

Cited by in corpus (1)

• All maximal gauged supergravities with uplift