Extended geometry and gauged maximal supergravity

Abstract

We consider generalized diffeomorphisms on an extended mega-space associated to the U-duality group of gauged maximal supergravity in four dimensions, E_7. Through the bein for the extended metric we derive dynamical (field-dependent) fluxes taking values in the representations allowed by supersymmetry, and obtain their quadratic constraints from gauge consistency conditions. A covariant generalized Ricci tensor is introduced, defined in terms of a connection for the generalized diffeomorphisms. We show that for any torsionless and metric-compatible generalized connection, the Ricci scalar reproduces the scalar potential of gauged maximal supergravity. We comment on how these results extend to other groups and dimensions.

41 pages. v2,v3: minor changes and references added

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Cited by in corpus (104)

• Exceptional Field Theory I: $E_{6(6)}$ covariant Form of M-Theory and Type IIB
• Exceptional Field Theory III: E${}_{8(8)}$
• Exploring Double Field Theory
• Exceptional Field Theory II: E${}_{7(7)}$
• Consistent Kaluza-Klein Truncations via Exceptional Field Theory
• Covariant action for a string in doubled yet gauged spacetime
• Consistent Type IIB Reductions to Maximal 5D Supergravity
• Supersymmetric E${}_{7(7)}$ Exceptional Field Theory
• Generalised geometry for string corrections
• M-theory and Type IIB from a Duality Manifest Action
• Geometry and fluxes of SL(5) exceptional field theory
• Comments on double field theory and diffeomorphisms
• The Odd story of ${\alpha }^{\prime }$-corrections
• Supersymmetry for Gauged Double Field Theory and Generalised Scherk-Schwarz Reductions
• The exceptional story of massive IIA supergravity
• Exceptional generalised geometry for massive IIA and consistent reductions
• Type II origin of dyonic gaugings
• Generalized Metric Formulation of 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
• Generalized gravity from modified DFT
• Duality Symmetric String and M-Theory
• Effective actions of non-geometric fivebranes
• The gauge structure of Exceptional Field Theories and the tensor hierarchy
• Strings and Branes are Waves
• The Geometry, Branes and Applications of Exceptional Field Theory
• Generalised fluxes, Yang-Baxter deformations and the O(d,d) structure of non-abelian T-duality
• U-duality extension of Drinfel'd double
• Generalised Scherk-Schwarz reductions from gauged supergravity
• The geometry behind double geometry
• U-duality covariant gravity
• Generalised diffeomorphisms for E${}_9$
• Beyond E11
• Electric/magnetic duality and RG flows in AdS4/CFT3
• E${}_9$ exceptional field theory I. The potential
• Consistent Pauli reduction on group manifolds
• Supersymmetric Backgrounds and Generalised Special Holonomy
• Non-linear Kaluza-Klein theory for dual fields
• On supersymmetric E11 exceptional field theory
• E${}_{6(6)}$ Exceptional Field Theory: Review and Embedding of Type IIB
• E${}_9$ exceptional field theory II. The complete dynamics
• Dualising consistent IIA / IIB truncations
• Generalized Dualities and Higher Derivatives
• Non-associativity in non-geometric string and M-theory backgrounds, the algebra of octonions, and missing momentum modes
• M5 algebra and SO(5,5) duality
• Exceptional Calabi--Yau spaces: the geometry of $\mathcal{N}=2$ backgrounds with flux
• Double Field Theory at SL(2) angles
• The Classical Double Copy for M-theory from a Kerr-Schild Ansatz for Exceptional Field Theory
• On the moduli space of spontaneously broken N = 8 supergravity
• The exceptional generalised geometry of supersymmetric AdS flux backgrounds
• Type IIB flux vacua from G-theory II
• O(d+1,d+1) enhanced double field theory
• Conserved Currents of Double Field Theory
• A supersymmetric reduction on the three-sphere
• Type IIB flux vacua from G-theory I
• Uplifting non-compact gauged supergravities
• Exceptional geometry and Borcherds superalgebras
• The embedding tensor of Scherk-Schwarz flux compactifications from eleven dimensions
• Effective Action for Non-Geometric Fluxes from Duality Covariant Actions
• On the exceptional generalised Lie derivative for $d\ge 7$
• Tensor hierarchy algebras and extended geometry II: Gauge structure and dynamics
• $L_{\infty }$ algebras for extended geometry from Borcherds superalgebras
• E${}_{7(7)}$ Exceptional Field Theory in Superspace
• From Exceptional Field Theory to Heterotic Double Field Theory via K3
• Exotic Branes in Exceptional Field Theory: $E_{7(7)}$ and Beyond
• Cosmological Implications from O(D,D)
• Einstein-Cartan Calculus for Exceptional Geometry
• Generalized Parallelizable Spaces from Exceptional Field Theory
• $L_{\infty }$ algebras and Tensor Hierarchies in Exceptional Field Theory and Gauged Supergravity
• Lobotomy of Flux Compactifications
• Gaugings from E7 Extended Geometries
• U-gravity : $\mathbf{SL}(N)$
• Subsectors, Dynkin Diagrams and New Generalised Geometries
• Tensor hierarchy algebra extensions of over-extended Kac--Moody algebras
• Infinity-enhancing of Leibniz algebras
• Duality Twisted Reductions of Double Field Theory of Type II Strings
• All maximal gauged supergravities with uplift
• Finite Transformations in Doubled and Exceptional Space
• New N=1 AdS${}_4$ solutions of type IIB supergravity
• Maximal D=2 supergravities from higher dimensions
• A Kaluza-Klein Approach to Double and Exceptional Field Theory
• Teleparallelism in the algebraic approach to extended geometry
• Deformed graded Poisson structures, Generalized Geometry and Supergravity
• Gauge Transformation of Double Field Theory for Open String
• Positive mass theorem in extended supergravities
• Dimensional Reduction of the Generalized DBI
• Twistors and supertwistors for exceptional field theory
• Extended geometry of magical supergravities
• Infinite and finite consistent truncations on deformed generalised parallelisations
• Uplifts of maximal supergravities and transitions to non-geometric vacua
• Geometry of ${\mathbb{R}}^{+}\times E_{3(3)}$ Exceptional Field Theory and F-theory
• Inflation in maximal gauged supergravities
• The teleparallel complex
• Generalized Cartan Calculus in general dimension
• $L_{\infty }$ algebras for extended geometry
• Solution-generating transformations in duality-invariant theories and the fluid/gravity correspondence
• Covariant Fractons and Weitzenböck Torsion
• Double Field Theory on Group Manifolds in a Nutshell
• Reductions of Exceptional Field Theories
• Duality Covariant Solutions in Extended Field Theories
• Flux Backgrounds and Exceptional Generalised Geometry
• On Geometries and Monodromies for Branes of Codimension Two
• Exotic Aspects of Extended Field Theories
• Gaugings and other aspects in supergravity