U-duality covariant gravity

Abstract

We extend the techniques of double field theory to more general gravity theories and U-duality symmetries, having in mind applications to the complete D=11 supergravity. In this paper we work out a (3+3)-dimensional `U-duality covariantization' of D=4 Einstein gravity, in which the Ehlers group SL(2,R) is realized geometrically, acting in the 3 representation on half of the coordinates. We include the full (2+1)-dimensional metric, while the `internal vielbein' is a coset representative of SL(2,R)/SO(2) and transforms under gauge transformations via generalized Lie derivatives. In addition, we introduce a gauge connection of the `C-bracket', and a gauge connection of SL(2,R), albeit subject to constraints. The action takes the form of (2+1)-dimensional gravity coupled to a Chern-Simons-matter theory but encodes the complete D=4 Einstein gravity. We comment on generalizations, such as an `$E_{8(8)}$ covariantization' of M-theory.

36 pages, v2: refs. added, to appear in JHEP

References in corpus (11)

• Double Field Theory
• Generalised Geometry for M-Theory
• Double Field Theory: A Pedagogical Review
• The gauge algebra of double field theory and Courant brackets
• Generalized Geometry and M theory
• Differential geometry with a projection: Application to double field theory
• Gauged Double Field Theory
• Double Field Theory Formulation of Heterotic Strings
• Generalized E(7(7)) coset dynamics and D=11 supergravity
• Ramond-Ramond Cohomology and O(D,D) T-duality
• Gauged diffeomorphisms and hidden symmetries in Kaluza-Klein theories

Cited by in corpus (37)

• Exceptional Form of D=11 Supergravity
• Exceptional Field Theory I: $E_{6(6)}$ covariant Form of M-Theory and Type IIB
• Exceptional Field Theory III: E${}_{8(8)}$
• Exceptional Field Theory II: E${}_{7(7)}$
• Supersymmetric E${}_{7(7)}$ Exceptional Field Theory
• Exceptional field theory: $SL(5)$
• Exceptional field theory: $SO(5,5)$
• Tensor Hierarchy and Generalized Cartan Calculus in SL(3)$\times$SL(2) Exceptional Field Theory
• Green-Schwarz mechanism and ${\alpha }^{\prime }$-deformed Courant brackets
• Fermions and Supersymmetry in ${\mathrm{E}}_{6(6)}$ Exceptional Field Theory
• The gauge structure of Exceptional Field Theories and the tensor hierarchy
• Generalised diffeomorphisms for E${}_9$
• Generalised geometry from the ground up
• Extended geometries
• Exotic branes and non-geometric fluxes
• Dual Double Field Theory
• E${}_9$ exceptional field theory II. The complete dynamics
• Tri-vector deformations in $d=11$ supergravity
• Superalgebras, constraints and partition functions
• O(d+1,d+1) enhanced double field theory
• Leibniz-Chern-Simons Theory and Phases of Exceptional Field Theory
• Defect branes as Alice strings
• Tensor hierarchy algebras and extended geometry II: Gauge structure and dynamics
• $L_{\infty }$ algebras for extended geometry from Borcherds superalgebras
• Standard Model as a Double Field Theory
• Cosmological Implications from O(D,D)
• U-gravity : $\mathbf{SL}(N)$
• Subsectors, Dynkin Diagrams and New Generalised Geometries
• Consistent Kaluza-Klein truncations and two-dimensional gauged supergravity
• Generalized 11D supergravity equations from tri-vector deformations
• The E10 Wheeler-DeWitt operator at low levels
• On 10 dimensional Exceptional Drinfel'd Algebras
• $L_{\infty }$ algebras for extended geometry
• Ehlers symmetry in four dimensions
• Reductions of Exceptional Field Theories
• The M-algebra completes the hierarchy of Super-Exceptional Tangent Spaces
• Gauge field fluxes and Bianchi identities in extended field theories