Yoonji Suh (Sogang University)
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 12N(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.