The local symmetries of M-theory and their formulation in generalised geometry

Abstract

In the doubled field theory approach to string theory, the T-duality group is promoted to a manifest symmetry at the expense of replacing ordinary Riemannian geometry with generalised geometry on a doubled space. The local symmetries are then given by a generalised Lie derivative and its associated algebra. This paper constructs an analogous structure for M-theory. A crucial by-product of this is the derivation of the physical section condition for M-theory formulated in an extended space.

20 pages, v2: Author Name corrected, v3: typos corrected

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Cited by in corpus (115)

• The Spacetime of Double Field Theory: Review, Remarks, and Outlook
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• Extended geometry and gauged maximal supergravity
• On the Riemann Tensor in Double Field Theory
• Exotic Branes in String Theory
• Supersymmetric Double Field Theory: Stringy Reformulation of Supergravity
• 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
• N=1 Supersymmetric Double Field Theory
• 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
• Branes are Waves and Monopoles
• Global aspects of double geometry
• Supersymmetry for Gauged Double Field Theory and Generalised Scherk-Schwarz Reductions
• Gauge theory of Kaluza-Klein and winding modes
• Half-maximal supersymmetry from exceptional field theory
• Gauged supergravities in 5 and 6 dimensions from generalised Scherk-Schwarz reductions
• U-geometry : SL(5)
• Fermions and Supersymmetry in ${\mathrm{E}}_{6(6)}$ Exceptional Field Theory
• An Action for F-theory: $\mathrm{SL}(2)\times {\mathbb{R}}^{+}$ Exceptional Field Theory
• Generalized gravity from modified DFT
• The gauge structure of Exceptional Field Theories and the tensor hierarchy
• Effective actions of non-geometric fivebranes
• Strings and Branes are Waves
• Homogeneous Yang-Baxter deformations as generalized diffeomorphisms
• The Geometry, Branes and Applications of Exceptional Field Theory
• A Double Sigma Model for Double Field Theory
• Towards an invariant geometry of double field theory
• U-duality extension of Drinfel'd double
• Poisson-Lie U-duality in Exceptional Field Theory
• The geometry behind double geometry
• Loops in exceptional field theory
• U-duality covariant gravity
• E${}_{6(6)}$ Exceptional Drinfel'd Algebras
• Generalised geometry from the ground up
• Extended geometries
• Exotic branes and non-geometric fluxes
• T-duality and non-geometric solutions from double geometry
• Supersymmetric AdS${}_7$ and AdS${}_6$ vacua and their consistent truncations with vector multiplets
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• A master exceptional field theory
• Non-Riemannian geometry of M-theory
• SL(5) duality from canonical M2-brane
• Dualising consistent IIA / IIB truncations
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• Tri-vector deformations in $d=11$ supergravity
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• Double Field Theory Inspired Cosmology
• Classical Yang-Baxter equation from beta-supergravity
• The Exceptional Sigma Model
• The exceptional generalised geometry of supersymmetric AdS flux backgrounds
• Type IIB flux vacua from G-theory II
• Seeking the balance: Patching double and exceptional field theories
• Non-abelian tri-vector deformations in d=11 supergravity
• Double supergeometry
• E8 duality and dual gravity
• Timelike U-dualities in Generalised Geometry
• Exploring Exceptional Drinfeld Geometries
• Type IIB flux vacua from G-theory I
• Exceptional geometry and Borcherds superalgebras
• Effective Action for Non-Geometric Fluxes from Duality Covariant Actions
• Exotic branes in Exceptional Field Theory: the SL(5) duality group
• E${}_{7(7)}$ Exceptional Field Theory in Superspace
• Canonical formulation and conserved charges of double field theory
• From Exceptional Field Theory to Heterotic Double Field Theory via K3
• Einstein-Cartan Calculus for Exceptional Geometry
• Cosmological Implications from O(D,D)
• A note on large gauge transformations in double field theory
• Lobotomy of Flux Compactifications
• Cancellation of divergences up to three loops in exceptional field theory
• Generalized Parallelizable Spaces from Exceptional Field Theory
• On non-abelian U-duality of 11D backgrounds
• Subsectors, Dynkin Diagrams and New Generalised Geometries
• U-gravity : $\mathbf{SL}(N)$
• Locally non-geometric fluxes and missing momenta in M-theory
• Fluxes in Exceptional Field Theory and Threebrane Sigma-Models
• Type II strings are Exceptional
• p-Brane Actions and Higher Roytenberg Brackets
• Particle actions and brane tensions from double and exceptional geometry
• Open exceptional strings and D-branes
• AKSZ constructions for topological membranes on $G_2$-manifolds
• All maximal gauged supergravities with uplift
• New N=1 AdS${}_4$ solutions of type IIB supergravity
• O-folds: Orientifolds and Orbifolds in Exceptional Field Theory
• Symmetries of M-theory and free Lie superalgebras
• Geometric non-geometry
• A Kaluza-Klein Approach to Double and Exceptional Field Theory
• U-duality in three and four dimensions
• A geometric formulation of exceptional field theory
• Exceptional field theories, superparticles in an enlarged 11D superspace and higher spin theories
• Twistors and supertwistors for exceptional field theory
• Five-brane Current Algebras in Type II String Theories
• Finite Gauge Transformations and Geometry in Extended Field Theory
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• Exotic branes and mixed-symmetry potentials II: Duality rules and exceptional $p$-form gauge fields
• Exotic branes and mixed-symmetry potentials I: predictions from $E_{11}$ symmetry
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• Dualising consistent truncations
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