U-gravity : $\mathbf{SL}(N)$

Abstract

We construct a duality manifest gravitational theory for the special linear group, $\mathbf{SL}(N)$ with $N\ne 4$. The spacetime is formally extended, to have the dimension $\frac{1}{2}N(N-1)$, yet is `gauged'. Consequently the theory is subject to a section condition. We introduce a semi-covariant derivative and a semi-covariant `Riemann' curvature, both of which can be completely covariantized after symmetrizing or contracting the $\mathbf{SL}(N)$ vector indices properly. Fully covariant scalar and `Ricci' curvatures then constitute the action and the `Einstein' equation of motion. For $N\ge 5$, the section condition admits duality inequivalent two solutions, one $(N-1)$-dimensional and the other three-dimensional. In each case, the theory can describe not only Riemannian but also non-Riemannian backgrounds.

1+36 pages. Comments added. To appear in JHEP

References in corpus (22)

• Double Field Theory
• Doubled Geometry and T-Folds
• The gauge algebra of double field theory and Courant brackets
• Generalized Geometry and M theory
• Exceptional Field Theory I: $E_{6(6)}$ covariant Form of M-Theory and Type IIB
• Exceptional Field Theory III: E${}_{8(8)}$
• Differential geometry with a projection: Application to double field theory
• Gauged Double Field Theory
• Duality orbits of non-geometric fluxes
• Global Aspects of T-Duality, Gauged Sigma Models and T-Folds
• Lectures on Generalized Complex Geometry for Physicists
• E(11) and the Embedding Tensor
• M-theory and Type IIB from a Duality Manifest Action
• Ramond-Ramond Cohomology and O(D,D) T-duality
• Double field formulation of Yang-Mills theory
• Kac-Moody Spectrum of (Half-)Maximal Supergravities
• E11, generalised space-time and IIA string theory
• The gauge structure of Exceptional Field Theories and the tensor hierarchy
• E11, generalised space-time and IIA string theory; the R-R sector
• Constraints and the E10 Coset Model
• Low Level Representations for E10 and E11
• New Cosmological Signatures from Double Field Theory

Cited by in corpus (11)

• Exceptional field theory: $SL(5)$
• Exceptional field theory: $SO(5,5)$
• Branes are Waves and Monopoles
• Extended geometries
• Remarks on the non-Riemannian sector in Double Field Theory
• Exotic branes and non-geometric fluxes
• The Classical Double Copy for M-theory from a Kerr-Schild Ansatz for Exceptional Field Theory
• Exceptional geometry and Borcherds superalgebras
• Gauge Transformation of Double Field Theory for Open String
• Strings, Branes and the Self-dual Solutions of Exceptional Field Theory
• Duality Covariant Solutions in Extended Field Theories