Extended Drinfel'd algebras and non-Abelian duality

Abstract

A Drinfel'd algebra gives the systematic construction of generalized parallelizable spaces and this allows us to study an extended T-duality, known as the Poisson-Lie T-duality. Recently, in order to find a generalized U-duality, an extended Drinfel'd algebra (ExDA), called the Exceptional Drinfel'd algebra (EDA) was proposed and a natural extension of the usual U-duality was studied both in the context of supergravity and membrane theory. In this paper, we clarify the general structure of ExDAs and show that an ExDA always gives a generalized parallelizable space, which may be regarded as a group manifold with generalized Nambu-Lie structures. We also discuss generalized Yang-Baxter deformations that are based on coboundary ExDAs. As important examples, we consider the $E_{n(n)}$ EDA for $n\le 8$ and study various aspects, both in terms of M-theory and type IIB theory.

arXiv comment60 pages

References in corpus (41)

• Double Field Theory
• Generalized metric formulation of double field theory
• Superspace Duality in Low-Energy Superstrings
• Two-Vierbein Formalism for String-Inspired Axionic Gravity
• Yang-Baxter $\sigma$-models and dS/AdS T-duality
• Exceptional Form of D=11 Supergravity
• Exceptional Field Theory I: $E_{6(6)}$ covariant Form of M-Theory and Type IIB
• Maximal gauged supergravity in three dimensions
• Poisson-Lie T-duality and Loop Groups of Drinfeld Doubles
• Exceptional Field Theory III: E${}_{8(8)}$
• Exploring Double Field Theory
• $E_{11}$, SL(32) and Central Charges
• Poisson-Lie T-duality
• Consistent Kaluza-Klein Truncations via Exceptional Field Theory
• Target space supergeometry of $\eta$ and $\lambda$-deformed strings
• The E_{11} origin of all maximal supergravities
• $\eta$ and $\lambda$ deformations as $\mathcal{E}$-models
• The maximal D=5 supergravities
• E(11) and the Embedding Tensor
• Manifest Duality in Low-Energy Superstrings
• Very Extended $E_8$ and $A_8$ at low levels, Gravity and Supergravity
• The IIA, IIB and eleven dimensional theories and their common E_{11} origin
• Yang-Baxter $\sigma$-models, conformal twists, and noncommutative Yang-Mills theory
• Doubled aspects of generalised dualities and integrable deformations
• Canonical equivalence of non-isometric sigma models and Poisson-Lie T-duality
• Supergravities without an Action: Gauging the Trombone
• Maximal Supergravity from IIB Flux Compactifications
• Homogeneous Yang-Baxter deformations as generalized diffeomorphisms
• U-duality extension of Drinfel'd double
• Classical Yang-Baxter Equation from Supergravity
• E${}_{6(6)}$ Exceptional Drinfel'd Algebras
• Non-Abelian U-duality for membrane
• Double Field Theory at SL(2) angles
• E11, generalised space-time and equations of motion in four dimensions
• Classical Yang-Baxter equation from beta-supergravity
• Non-abelian tri-vector deformations in d=11 supergravity
• Membrane Duality Revisited
• On the exceptional generalised Lie derivative for $d\ge 7$
• On non-abelian U-duality of 11D backgrounds
• Connecting M-theory and type IIB parameterizations in Exceptional Field Theory
• Jacobi-Lie symmetry and Jacobi-Lie T-dual sigma models on group manifolds

Cited by in corpus (3)

• Poisson-Lie T-plurality for WZW backgrounds
• Extended Field Theories as higher Kaluza-Klein theories
• Half-maximal Extended Drinfel'd Algebras