Generalized Geometry and M theory

Abstract

We reformulate the Hamiltonian form of bosonic eleven dimensional supergravity in terms of an object that unifies the three-form and the metric. For the case of four spatial dimensions, the duality group is manifest and the metric and C-field are on an equal footing even though no dimensional reduction is required for our results to hold. One may also describe our results using the generalized geometry that emerges from membrane duality. The relationship between the twisted Courant algebra and the gauge symmetries of eleven dimensional supergravity are described in detail.

29 pages of Latex, v2 References added, typos fixed, v3 corrected kinetic term and references added

References in corpus (34)

• String Theory Dynamics In Various Dimensions
• Unity of Superstring Dualities
• Double Field Theory
• Generalized metric formulation of double field theory
• A Geometry for Non-Geometric String Backgrounds
• E_11 and M Theory
• Background independent action for double field theory
• U-duality and M-Theory
• Generalised Geometry for M-Theory
• Doubled Geometry and T-Folds
• E10 and a "small tension expansion" of M Theory
• The gauge algebra of double field theory and Courant brackets
• M-theory, exceptional generalised geometry and superpotentials
• Duality and the Signature of Space-Time
• T-duality, Generalized Geometry and Non-Geometric Backgrounds
• $E_{11}$, SL(32) and Central Charges
• Global Aspects of T-Duality, Gauged Sigma Models and T-Folds
• Exotic branes and non-geometric backgrounds
• Generalized E(7(7)) coset dynamics and D=11 supergravity
• Background Field Equations for the Duality Symmetric String
• Representations of G+++ and the role of space-time
• E_{11} origin of Brane charges and U-duality multiplets
• Duality and Moduli Spaces for Time-Like Reductions
• An exceptional geometry for d=11 supergravity?
• E(11)-extended spacetime and gauged supergravities
• Duality Symmetric Strings, Dilatons and O(d,d) Effective Actions
• U-dual fluxes and Generalized Geometry
• Conformal chiral boson models on twisted doubled tori and non-geometric string vacua
• Brane dynamics, central charges and E_{11}
• Hidden Symmetries, Central Charges and All That
• The string partition function in Hull's doubled formalism
• Topological branes, p-algebras and generalized Nahm equations
• From current algebras for p-branes to topological M-theory
• Generalised space-time and duality

Cited by in corpus (197)

• The Spacetime of Double Field Theory: Review, Remarks, and Outlook
• Supergravity as Generalised Geometry I: Type II Theories
• 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
• Double Field Theory of Type II Strings
• Stringy differential geometry, beyond Riemann
• Consistent Kaluza-Klein Truncations via Exceptional Field Theory
• Doubled α'-Geometry
• A ten-dimensional action for non-geometric fluxes
• Gauged Double Field Theory
• Duality orbits of non-geometric fluxes
• Duality Invariant Actions and Generalised Geometry
• Duality Invariant M-theory: Gauged supergravities and Scherk-Schwarz reductions
• The local symmetries of M-theory and their formulation in generalised geometry
• 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
• Non-Abelian T-duality and the AdS/CFT correspondence:new N=1 backgrounds
• 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
• Consistent Type IIB Reductions to Maximal 5D Supergravity
• N=1 Supersymmetric Double Field Theory
• Exceptional field theory: $SL(5)$
• M-theory and Type IIB from a Duality Manifest Action
• Exceptional field theory: $SO(5,5)$
• Geometry and fluxes of SL(5) exceptional field theory
• Comments on double field theory and diffeomorphisms
• Kerr-Schild Double Field Theory and Classical Double Copy
• Non-geometric backgrounds in string theory
• Incorporation of fermions into double field theory
• Ramond-Ramond Cohomology and O(D,D) T-duality
• The O_{D,D} Geometry of String Theory
• Branes are Waves and Monopoles
• Massive Type II in Double Field Theory
• Duality Invariance: From M-theory to Double Field Theory
• Non-geometric strings, symplectic gravity and differential geometry of Lie algebroids
• Tensor Hierarchy and Generalized Cartan Calculus in SL(3)$\times$SL(2) Exceptional Field Theory
• Global aspects of double geometry
• The Odd story of ${\alpha }^{\prime }$-corrections
• Gauge theory of Kaluza-Klein and winding modes
• Half-maximal supersymmetry from exceptional field theory
• The exceptional story of massive IIA supergravity
• 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
• Effective actions of non-geometric fivebranes
• The gauge structure of Exceptional Field Theories and the tensor hierarchy
• Generalized gravity from modified DFT
• 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
• Generalised Scherk-Schwarz reductions from gauged supergravity
• A non-relativistic limit of M-theory and 11-dimensional membrane Newton-Cartan geometry
• The geometry behind double geometry
• Loops in exceptional field theory
• Generalised geometry, eleven dimensions and E11
• Generalized IIB supergravity from exceptional field theory
• The Intriguing Structure of Non-geometric Frames in String Theory
• U-duality covariant gravity
• Generalised diffeomorphisms for E${}_9$
• Double Field Theory for Double D-branes
• E${}_{6(6)}$ Exceptional Drinfel'd Algebras
• Generalised geometry from the ground up
• Type II DFT solutions from Poisson-Lie T-duality/plurality
• Extended geometries
• E${}_9$ exceptional field theory I. The potential
• Exotic branes and non-geometric fluxes
• IIB Supergravity and the E6(6) covariant vector-tensor hierarchy
• T-duality and non-geometric solutions from double geometry
• Supersymmetric Backgrounds and Generalised Special Holonomy
• Exceptional Flux Compactifications
• Supersymmetric AdS${}_7$ and AdS${}_6$ vacua and their consistent truncations with vector multiplets
• Non-Riemannian geometry of M-theory
• A master exceptional field theory
• Dimensional Oxidation of Non-geometric Fluxes in Type II Orientifolds
• SL(5) duality from canonical M2-brane
• E${}_9$ exceptional field theory II. The complete dynamics
• E${}_{8(8)}$ Exceptional Field Theory: Geometry, Fermions and Supersymmetry
• Dualising consistent IIA / IIB truncations
• On supersymmetric E11 exceptional field theory
• Canonical approach to Courant brackets for D-branes
• Non-Abelian U-duality for membrane
• 7-dimensional $\mathcal{N}=2$ Consistent Truncations using $\mathrm{SL}(5)$ Exceptional Field Theory
• M5 algebra and SO(5,5) duality
• Five-brane actions in double field theory
• Exceptional Calabi--Yau spaces: the geometry of $\mathcal{N}=2$ backgrounds with flux
• E11, generalised space-time and equations of motion in four dimensions
• The Exceptional Sigma Model
• Seeking the balance: Patching double and exceptional field theories
• Weaving the Exotic Web
• The exceptional generalised geometry of supersymmetric AdS flux backgrounds
• The Classical Double Copy for M-theory from a Kerr-Schild Ansatz for Exceptional Field Theory
• Non-abelian tri-vector deformations in d=11 supergravity
• Branes in Extended Spacetime: Brane Worldvolume Theory Based on Duality Symmetry
• Double supergeometry
• E8 duality and dual gravity
• Exploring Exceptional Drinfeld Geometries
• Timelike U-dualities in Generalised Geometry
• Conserved Currents of Double Field Theory
• Polyvector deformations in eleven-dimensional supergravity
• Effective Action for Non-Geometric Fluxes from Duality Covariant Actions
• Leibniz-Chern-Simons Theory and Phases of Exceptional Field Theory
• Exceptional geometry and Borcherds superalgebras
• On the exceptional generalised Lie derivative for $d\ge 7$
• Tensor hierarchy algebras and extended geometry II: Gauge structure and dynamics
• The free energy of N=2 supersymmetric AdS_4 solutions of M-theory
• Toward Exotic 6D Supergravities
• $L_{\infty }$ algebras for extended geometry from Borcherds superalgebras
• Canonical formulation and conserved charges of double field theory
• E${}_{7(7)}$ Exceptional Field Theory in Superspace
• Exotic branes in Exceptional Field Theory: the SL(5) duality group
• Kaluza-Klein fermion mass matrices from Exceptional Field Theory and $\mathcal{N}=1$ spectra
• Exotic Branes in Exceptional Field Theory: $E_{7(7)}$ and Beyond
• From Exceptional Field Theory to Heterotic Double Field Theory via K3
• Asymptotic Flatness, Taub-NUT, and Variational Principle
• Cosmological Implications from O(D,D)
• Einstein-Cartan Calculus for Exceptional Geometry
• On current algebras, generalised fluxes and non-geometry
• A note on large gauge transformations in double field theory
• Higher Gauge Structures in Double and Exceptional Field Theory
• Lobotomy of Flux Compactifications
• Generalized Parallelizable Spaces from Exceptional Field Theory
• Entanglement with Centers
• Cancellation of divergences up to three loops in exceptional field theory
• $L_{\infty }$ algebras and Tensor Hierarchies in Exceptional Field Theory and Gauged Supergravity
• Aspects of the Doubled Worldsheet
• On non-abelian U-duality of 11D backgrounds
• Exceptional M-brane sigma models and $\eta$-symbols
• Supersymmetric spectroscopy on AdS${}_4\times S^7$ and AdS${}_4\times S^6$
• Locally non-geometric fluxes and missing momenta in M-theory
• Subsectors, Dynkin Diagrams and New Generalised Geometries
• U-gravity : $\mathbf{SL}(N)$
• Doubled strings, negative strings and null waves
• Super-Chern-Simons spectra from Exceptional Field Theory
• Tensor hierarchy algebra extensions of over-extended Kac--Moody algebras
• Generalised vielbeins and non-linear realisations
• Equations of Motion in Double Field Theory: From Particles to Scale Factors
• Fluxes in Exceptional Field Theory and Threebrane Sigma-Models
• Born sigma model for branes in exceptional geometry
• Type II strings are Exceptional
• Particle actions and brane tensions from double and exceptional geometry
• p-Brane Actions and Higher Roytenberg Brackets
• E11 and exceptional field theory
• Discreteness of time in the evolution of the universe
• AKSZ constructions for topological membranes on $G_2$-manifolds
• Currents, charges and algebras in exceptional generalised geometry
• All maximal gauged supergravities with uplift
• Duality Twisted Reductions of Double Field Theory of Type II Strings
• Open exceptional strings and D-branes
• One-Loop $\beta$ Function of the Double Sigma Model with Constant Background
• Maximal D=2 supergravities from higher dimensions
• O-folds: Orientifolds and Orbifolds in Exceptional Field Theory
• A geometric formulation of exceptional field theory
• A Kaluza-Klein Approach to Double and Exceptional Field Theory
• Generalized 11D supergravity equations from tri-vector deformations
• Extended generalized geometry and a DBI-type effective action for branes ending on branes
• U-duality in three and four dimensions
• Teleparallelism in the algebraic approach to extended geometry
• Dimensional Reduction of the Generalized DBI
• Boundary Conditions and the Generalized Metric Formulation of the Double Sigma Model
• Classification of M2-brane 2-torus bundles, U-duality invariance and type II gauged supergravities
• Exceptional field theories, superparticles in an enlarged 11D superspace and higher spin theories
• Twistors and supertwistors for exceptional field theory
• Finite Gauge Transformations and Geometry in Extended Field Theory
• Perturbative F-theory 10-brane and M-theory 5-brane
• Infinite and finite consistent truncations on deformed generalised parallelisations
• Electric-Magnetic Dualities in Non-Abelian and Non-Commutative Gauge Theories
• Charting the Conformal Manifold of Holographic CFT${}_2$'s
• Extended geometry of magical supergravities
• Lie algebroids, non-associative structures and non-geometric fluxes
• Uplifts of maximal supergravities and transitions to non-geometric vacua
• Geometry of ${\mathbb{R}}^{+}\times E_{3(3)}$ Exceptional Field Theory and F-theory
• The teleparallel complex
• Tri-vector deformations with external fluxes
• $L_{\infty }$ algebras for extended geometry
• SUSY and tri-vector deformations
• 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
• N-Extended Lorentzian Kac-Moody algebras
• Gravitational Core of Double Field Theory: Lecture Notes
• Reductions of Exceptional Field Theories
• Dualising consistent truncations
• Double Field Theory and Pseudo-Supersymmetry
• Pre-NQ Manifolds and Correspondence Spaces: the Nilmanifold Example
• Duality rules for more mixed-symmetry potentials
• Brane Symmetries Revisited: Symmetries of Tensile and Tensionless Branes in Possibly Degenerate Metrics and their Manifestations
• A T-Fold Black Hole in Doubled Type IIB