Duality Invariant Actions and Generalised Geometry

Abstract

We construct the non-linear realisation of the semi-direct product of E(11) and its first fundamental representation at lowest order and appropriate to spacetime dimensions four to seven. This leads to a non-linear realisation of the duality groups and introduces fields that depend on a generalised space which possess a generalised vielbein. We focus on the part of the generalised space on which the duality groups alone act and construct an invariant action.

59 pages (typos fixed and added comments)

References in corpus (14)

• Double Field Theory
• Generalised Geometry for M-Theory
• The gauge algebra of double field theory and Courant brackets
• Generalized Geometry and M theory
• The E_{11} origin of all maximal supergravities
• SO(5,5) duality in M-theory and generalized geometry
• The local symmetries of M-theory and their formulation in generalised geometry
• E(11) and the Embedding Tensor
• Generalized E(7(7)) coset dynamics and D=11 supergravity
• Boundary Terms in Generalized Geometry and doubled field theory
• Dual fields and E_{11}
• E11, generalised space-time and IIA string theory
• The E(11) origin of all maximal supergravities - the hierarchy of field-strengths
• Local E(11)

Cited by in corpus (118)

• The Spacetime of Double Field Theory: Review, Remarks, and Outlook
• Exceptional Form of D=11 Supergravity
• Exceptional Field Theory I: $E_{6(6)}$ covariant Form of M-Theory and Type IIB
• The gauge structure of generalised diffeomorphisms
• Exploring Double Field Theory
• Exceptional Field Theory II: E${}_{7(7)}$
• Consistent Kaluza-Klein Truncations via Exceptional Field Theory
• Gauged Double Field Theory
• Duality orbits of non-geometric fluxes
• Duality Invariant M-theory: Gauged supergravities and Scherk-Schwarz reductions
• Extended geometry and gauged maximal supergravity
• On the Riemann Tensor in Double Field Theory
• Exotic Branes in String Theory
• Large Gauge Transformations in Double Field Theory
• Covariant action for a string in doubled yet gauged spacetime
• Stringy Unification of Type IIA and IIB Supergravities under N=2 D=10 Supersymmetric Double Field Theory
• Non-Geometric Fluxes in Supergravity and Double Field Theory
• Supersymmetric E${}_{7(7)}$ Exceptional Field Theory
• N=1 Supersymmetric Double Field Theory
• Exceptional field theory: $SL(5)$
• M-theory and Type IIB from a Duality Manifest Action
• Exceptional field theory: $SO(5,5)$
• Comments on double field theory and diffeomorphisms
• Geometry and fluxes of SL(5) exceptional field theory
• Kerr-Schild Double Field Theory and Classical Double Copy
• Ramond-Ramond Cohomology and O(D,D) T-duality
• The O_{D,D} Geometry of String Theory
• Branes are Waves and Monopoles
• Global aspects of double geometry
• Tensor Hierarchy and Generalized Cartan Calculus in SL(3)$\times$SL(2) Exceptional Field Theory
• Supersymmetry for Gauged Double Field Theory and Generalised Scherk-Schwarz Reductions
• Gauge theory of Kaluza-Klein and winding modes
• Gauged supergravities in 5 and 6 dimensions from generalised Scherk-Schwarz reductions
• U-geometry : SL(5)
• An Action for F-theory: $\mathrm{SL}(2)\times {\mathbb{R}}^{+}$ Exceptional Field Theory
• Fermions and Supersymmetry in ${\mathrm{E}}_{6(6)}$ Exceptional Field Theory
• Generalized gravity from modified DFT
• The gauge structure of Exceptional Field Theories and the tensor hierarchy
• Strings and Branes are Waves
• Homogeneous Yang-Baxter deformations as generalized diffeomorphisms
• The Geometry, Branes and Applications of Exceptional Field Theory
• U-duality extension of Drinfel'd double
• A Unique Connection for Born Geometry
• The geometry behind double geometry
• Generalised geometry from the ground up
• Type II DFT solutions from Poisson-Lie T-duality/plurality
• Extended geometries
• Exotic branes and non-geometric fluxes
• IIB Supergravity and the E6(6) covariant vector-tensor hierarchy
• Supersymmetric Backgrounds and Generalised Special Holonomy
• T-duality and non-geometric solutions from double geometry
• Non-Riemannian geometry of M-theory
• SL(5) duality from canonical M2-brane
• E${}_{8(8)}$ Exceptional Field Theory: Geometry, Fermions and Supersymmetry
• Tri-vector deformations in $d=11$ supergravity
• M5 algebra and SO(5,5) duality
• E11, generalised space-time and equations of motion in four dimensions
• Exceptional Calabi--Yau spaces: the geometry of $\mathcal{N}=2$ backgrounds with flux
• The Classical Double Copy for M-theory from a Kerr-Schild Ansatz for Exceptional Field Theory
• The Exceptional Sigma Model
• Weaving the Exotic Web
• The exceptional generalised geometry of supersymmetric AdS flux backgrounds
• Classical Yang-Baxter equation from beta-supergravity
• Type IIB flux vacua from G-theory II
• Branes in Extended Spacetime: Brane Worldvolume Theory Based on Duality Symmetry
• Double supergeometry
• E8 duality and dual gravity
• Timelike U-dualities in Generalised Geometry
• Polyvector deformations in eleven-dimensional supergravity
• Type IIB flux vacua from G-theory I
• Generalised Space-time and Gauge Transformations
• Effective Action for Non-Geometric Fluxes from Duality Covariant Actions
• Exceptional geometry and Borcherds superalgebras
• On the exceptional generalised Lie derivative for $d\ge 7$
• Exotic branes in Exceptional Field Theory: the SL(5) duality group
• World-volume Effective Action of Exotic Five-brane in M-theory
• Exotic Branes in Exceptional Field Theory: $E_{7(7)}$ and Beyond
• Einstein-Cartan Calculus for Exceptional Geometry
• A note on large gauge transformations in double field theory
• Non-abelian U-duality at work
• Generalized Parallelizable Spaces from Exceptional Field Theory
• Higher Gauge Structures in Double and Exceptional Field Theory
• Lobotomy of Flux Compactifications
• $L_{\infty }$ algebras and Tensor Hierarchies in Exceptional Field Theory and Gauged Supergravity
• Exceptional M-brane sigma models and $\eta$-symbols
• T-duality, Quotients and Currents for Non-Geometric Closed Strings
• Subsectors, Dynkin Diagrams and New Generalised Geometries
• U-gravity : $\mathbf{SL}(N)$
• Generalised vielbeins and non-linear realisations
• Fluxes in Exceptional Field Theory and Threebrane Sigma-Models
• Born sigma model for branes in exceptional geometry
• Particle actions and brane tensions from double and exceptional geometry
• Type II strings are Exceptional
• All maximal gauged supergravities with uplift
• Currents, charges and algebras in exceptional generalised geometry
• AKSZ constructions for topological membranes on $G_2$-manifolds
• Symmetries of M-theory and free Lie superalgebras
• A geometric formulation of exceptional field theory
• U-duality in three and four dimensions
• A Kaluza-Klein Approach to Double and Exceptional Field Theory
• Generalized 11D supergravity equations from tri-vector deformations
• Twistors and supertwistors for exceptional field theory
• Finite Gauge Transformations and Geometry in Extended Field Theory
• An E11 invariant gauge fixing
• Generalised U-dual solutions via ISO(7) gauged supergravity
• On 10 dimensional Exceptional Drinfel'd Algebras
• Geometry of ${\mathbb{R}}^{+}\times E_{3(3)}$ Exceptional Field Theory and F-theory
• Exotic potentials and Bianchi identities in SL(5) exceptional field theory
• Exotic branes and mixed-symmetry potentials I: predictions from $E_{11}$ symmetry
• Exotic branes and mixed-symmetry potentials II: Duality rules and exceptional $p$-form gauge fields
• Reductions of Exceptional Field Theories
• Non-isometric U-dualities
• M2- and M5-branes in E11 Current Algebra Formulation of M-theory
• Pre-NQ Manifolds and Correspondence Spaces: the Nilmanifold Example
• Duality rules for more mixed-symmetry potentials
• Generalised U-dual solutions in supergravity
• Algebraic structures in exceptional geometry
• Localized Kaluza-Klein 6-brane