U-duality extension of Drinfel'd double

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., ${\hat{\mathcal{L}}}_{E_A}{E}_B{}^I=-{\mathcal{F}}_{AB}{}^C{E}_C{}^I$. 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.

arXiv comment34 pages; v2: references added, expanded the discussion of the Yang-Baxter deformation; v3: a reference added, typos corrected, to appear in PTEP; v4: footnotes 5 and 8 added, a redundant condition in Eq.(6.20) removed

References in corpus (69)

• Double Field Theory
• On Foundation of the Generalized Nambu Mechanics
• Generalized metric formulation of double field theory
• Superspace Duality in Low-Energy Superstrings
• Two-Vierbein Formalism for String-Inspired Axionic Gravity
• E_11 and M Theory
• On integrability of the Yang-Baxter $\si$-model
• An integrable deformation of the AdS_5 x S^5 superstring action
• Duality Symmetries from Non--Abelian Isometries in String Theories
• Dual Non-Abelian Duality and the Drinfeld Double
• Yang-Baxter $\sigma$-models and dS/AdS T-duality
• On classical q-deformations of integrable sigma-models
• Generalized Geometry and M theory
• Exceptional Form of D=11 Supergravity
• Exceptional Field Theory I: $E_{6(6)}$ covariant Form of M-Theory and Type IIB
• Double Field Theory and N=4 Gauged Supergravity
• Exceptional Field Theory III: E${}_{8(8)}$
• The gauge structure of generalised diffeomorphisms
• Exploring Double Field Theory
• $E_{11}$, SL(32) and Central Charges
• Scale invariance of the eta-deformed AdS5 x S5 superstring, T-duality and modified type II equations
• Jordanian deformations of the AdS_5xS^5 superstring
• Poisson-Lie T-duality
• Exceptional Field Theory II: E${}_{7(7)}$
• On Nonabelian Duality
• On Non-Abelian Duality
• Gauged Double Field Theory
• Target space supergeometry of $\eta$ and $\lambda$-deformed strings
• The E_{11} origin of all maximal supergravities
• SO(5,5) duality in M-theory and generalized geometry
• Duality Invariant Actions and Generalised Geometry
• The local symmetries of M-theory and their formulation in generalised geometry
• Extended geometry and gauged maximal supergravity
• Manifest Duality in Low-Energy Superstrings
• The IIA, IIB and eleven dimensional theories and their common E_{11} origin
• A Problem with Non-Abelian Duality
• M-theory and Type IIB from a Duality Manifest Action
• Kappa-symmetry of superstring sigma model and generalized 10d supergravity equations
• Poisson-Lie T-Duality in Double Field Theory
• Geometry and fluxes of SL(5) exceptional field theory
• Doubled aspects of generalised dualities and integrable deformations
• Canonical equivalence of non-isometric sigma models and Poisson-Lie T-duality
• Poisson-Lie T-plurality
• E(11)-extended spacetime and gauged supergravities
• The exceptional story of massive IIA supergravity
• Double Field Theory on Group Manifolds
• Generalized Metric Formulation of Double Field Theory on Group Manifolds
• The gauge structure of Exceptional Field Theories and the tensor hierarchy
• Generalized gravity from modified DFT
• Homogeneous Yang-Baxter deformations as generalized diffeomorphisms
• Classification of 6-dimensional real Drinfeld doubles
• Generalised Scherk-Schwarz reductions from gauged supergravity
• Generalised geometry, eleven dimensions and E11
• Generalized IIB supergravity from exceptional field theory
• Type II DFT solutions from Poisson-Lie T-duality/plurality
• A Survey on Nambu-Poisson Brackets
• Tri-vector deformations in $d=11$ supergravity
• E11, generalised space-time and equations of motion in four dimensions
• Generalised space-time and duality
• E_{11}, ten forms and supergravity
• Flux Formulation of DFT on Group Manifolds and Generalized Scherk-Schwarz Compactifications
• Non-Abelian T-duality as a Transformation in Double Field Theory
• Generalized Parallelizable Spaces from Exceptional Field Theory
• Doubled Aspects of Vaisman Algebroid and Gauge Symmetry in Double Field Theory
• E(7(7)) and d=11 supergravity
• Fluxes in Exceptional Field Theory and Threebrane Sigma-Models
• Connecting M-theory and type IIB parameterizations in Exceptional Field Theory
• Duality Twisted Reductions of Double Field Theory of Type II Strings
• Massive Deformations of Type IIA Theory Within Double Field Theory

Cited by in corpus (34)

• The Geometry, Branes and Applications of Exceptional Field Theory
• Poisson-Lie U-duality in Exceptional Field Theory
• E${}_{6(6)}$ Exceptional Drinfel'd Algebras
• Non-Abelian U-duality for membrane
• Non-abelian tri-vector deformations in d=11 supergravity
• Exploring Exceptional Drinfeld Geometries
• Polyvector deformations in eleven-dimensional supergravity
• G-algebroids: a unified framework for exceptional and generalised geometry, and Poisson-Lie duality
• Non-abelian U-duality at work
• On non-abelian U-duality of 11D backgrounds
• Consistent Truncations and Dualities
• Exceptional algebroids and type IIB superstrings
• Global Aspects of Doubled Geometry and Pre-rackoid
• All maximal gauged supergravities with uplift
• Currents, charges and algebras in exceptional generalised geometry
• Generalized Dualities and Supergroups
• More on Doubled Aspects of Algebroids in Double Field Theory
• Generalizing eleven-dimensional supergravity
• Jacobi-Lie T-plurality
• Tri-vector deformations on compact isometries
• Generalised U-dual solutions via ISO(7) gauged supergravity
• On 10 dimensional Exceptional Drinfel'd Algebras
• Towards an extended/higher correspondence -- Generalised geometry, bundle gerbes and global Double Field Theory
• Extended Drinfel'd algebras and non-Abelian duality
• Integrability structures in string theory
• Y-algebroids and $E_{7(7)}\times {\mathbb{R}}^{+}$-generalised geometry
• Poisson-Lie T-plurality for dressing cosets
• Jacobi-Lie Models and Supergravity Equations
• Poisson-Lie T-plurality for WZW backgrounds
• T-folds as Poisson-Lie plurals
• Classification of six-dimensional Leibniz algebras ${\mathcal E}_3
• Non-isometric U-dualities
• Half-maximal Extended Drinfel'd Algebras
• Extended Field Theories as higher Kaluza-Klein theories