# CERN-CKC TH Institute on Duality Symmetries in String and M-Theories

Aug 3 – 14, 2015
CERN
Europe/Zurich timezone

## U-gravity for SL(N)

Aug 13, 2015, 2:00 PM
1h
4-3-006 - TH Conference Room (CERN)

### Speaker

Yoonji Suh (Sogang University)

### Description

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.