Exceptional Field Theory III: E${}_{8(8)}$

Abstract

We develop exceptional field theory for E${}_{8(8)}$, defined on a (3+248)-dimensional generalized spacetime with extended coordinates in the adjoint representation of E${}_{8(8)}$. The fields transform under E${}_{8(8)}$ generalized diffeomorphisms and are subject to covariant section constraints. The bosonic fields include an `internal' dreibein and an E${}_{8(8)}$-valued `zweihundertachtundvierzigbein' (248-bein). Crucially, the theory also features gauge vectors for the E${}_{8(8)}$ E-bracket governing the generalized diffeomorphism algebra and covariantly constrained gauge vectors for a separate but constrained E${}_{8(8)}$ gauge symmetry. The complete bosonic theory, with a novel Chern-Simons term for the gauge vectors, is uniquely determined by gauge invariance under internal and external generalized diffeomorphisms. The theory consistently comprises components of the dual graviton encoded in the 248-bein. Upon picking particular solutions of the constraints the theory reduces to D=11 or type IIB supergravity, for which the dual graviton becomes pure gauge. This resolves the dual graviton problem, as we discuss in detail.

26 pages, v2: published version

References in corpus (34)

• Double Field Theory
• Generalized metric formulation of double field theory
• Superspace Duality in Low-Energy Superstrings
• E_11 and M Theory
• Background independent action for double field theory
• Dualisation of Dualities, I
• New Formulations of D=10 Supersymmetry and D8-O8 Domain Walls
• The gauge algebra of double field theory and Courant brackets
• 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
• Maximal gauged supergravity in three dimensions
• The gauge structure of generalised diffeomorphisms
• $E_{11}$, SL(32) and Central Charges
• Double Field Theory of Type II Strings
• Exceptional Field Theory II: E${}_{7(7)}$
• Gauged maximal supergravities and hierarchies of nonabelian vector-tensor systems
• Unification of Type II Strings and T-duality
• Gauged Supergravities, Tensor Hierarchies, and M-Theory
• Extended geometry and gauged maximal supergravity
• Duality in Gravity and Higher Spin Gauge Fields
• Strongly Coupled Gravity and Duality
• Consistent deformations of dual formulations of linearized gravity: A no-go result
• Supersymmetric E${}_{7(7)}$ Exceptional Field Theory
• Frame-like Geometry of Double Field Theory
• M-theory and Type IIB from a Duality Manifest Action
• No Self-Interaction for Two-Column Massless Fields
• An exceptional geometry for d=11 supergravity?
• Gauge theory of Kaluza-Klein and winding modes
• Chern-Simons vs. Yang-Mills gaugings in three dimensions
• U-duality covariant gravity
• Non-linear parent action and dual gravity
• On the Yangian Y(e_8) quantum symmetry of maximal supergravity in two dimensions
• E8 duality and dual gravity

Cited by in corpus (145)

• Exceptional Field Theory I: $E_{6(6)}$ covariant Form of M-Theory and Type IIB
• Consistent Kaluza-Klein Truncations via Exceptional Field Theory
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• Supersymmetric E${}_{7(7)}$ Exceptional Field Theory
• Generalised geometry for string corrections
• Exceptional field theory: $SL(5)$
• Exceptional field theory: $SO(5,5)$
• Geometry and fluxes of SL(5) exceptional field theory
• Non-geometric backgrounds in string theory
• Branes are Waves and Monopoles
• Tensor Hierarchy and Generalized Cartan Calculus in SL(3)$\times$SL(2) Exceptional Field Theory
• Half-maximal supersymmetry from exceptional field theory
• Double Field Theory on Group Manifolds
• 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
• Kaluza-Klein Spectrometry from Exceptional Field Theory
• Generalized gravity from modified DFT
• Systematics of consistent truncations from generalised geometry
• Duality Symmetric String and M-Theory
• Homogeneous Yang-Baxter deformations as generalized diffeomorphisms
• The Geometry, Branes and Applications of Exceptional Field Theory
• U-duality extension of Drinfel'd double
• Generalised Scherk-Schwarz reductions from gauged supergravity
• A non-relativistic limit of M-theory and 11-dimensional membrane Newton-Cartan geometry
• Loops in exceptional field theory
• Generalised diffeomorphisms for E${}_9$
• Beyond E11
• E${}_9$ exceptional field theory I. The potential
• Exotic branes and non-geometric fluxes
• Consistent Pauli reduction on group manifolds
• IIB Supergravity and the E6(6) covariant vector-tensor hierarchy
• Supersymmetric Backgrounds and Generalised Special Holonomy
• Non-Riemannian geometry of M-theory
• A master exceptional field theory
• Dual Double Field Theory
• E${}_{6(6)}$ Exceptional Field Theory: Review and Embedding of Type IIB
• Dualising consistent IIA / IIB truncations
• E${}_{8(8)}$ Exceptional Field Theory: Geometry, Fermions and Supersymmetry
• E${}_9$ exceptional field theory II. The complete dynamics
• Non-Abelian U-duality for membrane
• Double Field Theory at SL(2) angles
• Superalgebras, constraints and partition functions
• Exceptional Calabi--Yau spaces: the geometry of $\mathcal{N}=2$ backgrounds with flux
• The Exceptional Sigma Model
• Weaving the Exotic Web
• The Classical Double Copy for M-theory from a Kerr-Schild Ansatz for Exceptional Field Theory
• E11 must be a symmetry of strings and branes
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• Leibniz Gauge Theories and Infinity Structures
• Double supergeometry
• Global Properties of the Conformal Manifold for S-Fold Backgrounds
• Conserved Currents of Double Field Theory
• Superstring in doubled superspace
• Membrane Duality Revisited
• More on the Hidden Symmetries of 11D Supergravity
• Generalised Space-time and Gauge Transformations
• Exceptional geometry and Borcherds superalgebras
• S-folds and holographic RG flows on the D3-brane
• Leibniz-Chern-Simons Theory and Phases of Exceptional Field Theory
• Effective Action for Non-Geometric Fluxes from Duality Covariant Actions
• Tensor hierarchy algebras and extended geometry II: Gauge structure and dynamics
• $L_{\infty }$ algebras for extended geometry from Borcherds superalgebras
• On the exceptional generalised Lie derivative for $d\ge 7$
• E${}_{7(7)}$ Exceptional Field Theory in Superspace
• Exotic branes in Exceptional Field Theory: the SL(5) duality group
• $\mathcal{N}=(8,0)$ AdS vacua of three-dimensional supergravity
• Kaluza-Klein spectrometry for $\mathrm{Ad}{\mathrm{S}}_3$ vacua
• Exotic Branes in Exceptional Field Theory: $E_{7(7)}$ and Beyond
• Ten-dimensional origin of Minkowski vacua in $\mathcal{N}=8$ supergravity
• $L_{\infty }$ algebras and Tensor Hierarchies in Exceptional Field Theory and Gauged Supergravity
• Cancellation of divergences up to three loops in exceptional field theory
• Lobotomy of Flux Compactifications
• Higher Gauge Structures in Double and Exceptional Field Theory
• Generalized Parallelizable Spaces from Exceptional Field Theory
• Exceptional M-brane sigma models and $\eta$-symbols
• A fresh view on string orbifolds
• U-gravity : $\mathbf{SL}(N)$
• Critical Super F-theories
• New gaugings and non-geometry
• Tensor hierarchy algebra extensions of over-extended Kac--Moody algebras
• Fluxes in Exceptional Field Theory and Threebrane Sigma-Models
• On symmetries and dynamics of exotic supermultiplets
• Born sigma model for branes in exceptional geometry
• Type II strings are Exceptional
• Particle actions and brane tensions from double and exceptional geometry
• Infinity-enhancing of Leibniz algebras
• E11 and exceptional field theory
• Consistent truncations in higher derivative supergravity
• All maximal gauged supergravities with uplift
• Currents, charges and algebras in exceptional generalised geometry
• Open exceptional strings and D-branes
• One-Loop $\beta$ Function of the Double Sigma Model with Constant Background
• Towards Weakly Constrained Double Field Theory
• The higher-dimensional origin of five-dimensional $\mathcal{N}=2$ gauged supergravities
• Connecting M-theory and type IIB parameterizations in Exceptional Field Theory
• Finite Transformations in Doubled and Exceptional Space
• Maximal D=2 supergravities from higher dimensions
• Consistent truncations to 3-dimensional supergravity
• New N=1 AdS${}_4$ solutions of type IIB supergravity
• Teleparallelism in the algebraic approach to extended geometry
• A Kaluza-Klein Approach to Double and Exceptional Field Theory
• A geometric formulation of exceptional field theory
• Gauge Transformation of Double Field Theory for Open String
• Dimensional Reduction of the Generalized DBI
• Boundary Conditions and the Generalized Metric Formulation of the Double Sigma Model
• Exceptional field theories, superparticles in an enlarged 11D superspace and higher spin theories
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• Twistors and supertwistors for exceptional field theory
• Extended geometry of magical supergravities
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• F-theory with zeroth-quantized ghosts
• Charting the Conformal Manifold of Holographic CFT${}_2$'s
• On Stringy de Sitter Spacetimes
• Uplifts of maximal supergravities and transitions to non-geometric vacua
• On section conditions of E7(7) exceptional field theory and superparticle in N=8 central charge superspace
• Notophs of N = 8 supergravity
• The teleparallel complex
• Generalized Cartan Calculus in general dimension
• Geometry of ${\mathbb{R}}^{+}\times E_{3(3)}$ Exceptional Field Theory and F-theory
• Extended Drinfel'd algebras and non-Abelian duality
• Strings, Branes and the Self-dual Solutions of Exceptional Field Theory
• Exotic Brane Junctions from F-theory
• Reviving 3D $\mathcal{N}=8$ superconformal field theories
• Classical worldvolumes as generalised geodesics
• Y-algebroids and $E_{7(7)}\times {\mathbb{R}}^{+}$-generalised geometry
• Ehlers symmetry in four dimensions
• Higher curvature Bianchi identities, generalised geometry and $L_{\infty }$ algebras
• $L_{\infty }$ algebras for extended geometry
• M Theory from F Theory
• Reductions of Exceptional Field Theories
• Exotic branes and mixed-symmetry potentials II: Duality rules and exceptional $p$-form gauge fields
• Open F-branes
• Supergravity Fluxes and Generalised Geometry
• Aspects of electric-magnetic dualities in maximal supergravity
• The M-algebra completes the hierarchy of Super-Exceptional Tangent Spaces
• The landscape of G-structures in eight-manifold compactifications of M-theory
• The many facets of exceptional field theory
• $\eta$-symbols in exceptional field theory
• Double Field Theory and Pseudo-Supersymmetry
• Duality rules for more mixed-symmetry potentials
• Localized Kaluza-Klein 6-brane
• The canonical formulation of E${}_{6(6)}$ exceptional field theory
• Half-maximal Extended Drinfel'd Algebras
• Algebraic structures in exceptional geometry