2014/02/28 by Jeong-Hyuck Park, Yoonji Suh · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Covariant derivative #Covariant transformation #Curvature #Dimension (graph theory) #Duality (order theory) #Geometry #Gravitation #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum mechanics #Ricci curvature #Riemann curvature tensor #Riemann hypothesis #Scalar (mathematics) #Scalar curvature #Spacetime #hep-th #math.DG
paper · pdf · doi:10.1007/jhep06(2014)102
published as JHEP 1406 (2014) 102 · 1+36 pages. Comments added. To appear in JHEP
arxiv created 2014/05/27 · openalex publication_date 2014/06/01 · arxiv updated 2014/07/08 · openalex created_date 2020/11/23 · openalex updated_date 2026/06/19
We construct a duality manifest gravitational theory for the special linear group, SL(N) with N ≠ 4. The spacetime is formally extended, to have the dimension (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 SL(N) vector indices properly. Fully covariant scalar and ‘Ricci’ curvatures then constitute the action and the ‘Einstein’ equation of motion. For N ≥ 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.