U-geometry : SL(5)
High Energy Physics - Theory
2013-11-13 v3 Differential Geometry
Abstract
Recently Berman and Perry constructed a four-dimensional M-theory effective action which manifests SL(5) U-duality. Here we propose an underlying differential geometry of it, under the name `SL(5) U-geometry' which generalizes the ordinary Riemannian geometry in an SL(5) compatible manner. We introduce a `semi-covariant' derivative that can be converted into fully covariant derivatives after anti-symmetrizing or contracting the SL(5) vector indices appropriately. We also derive fully covariant scalar and Ricci-like curvatures which constitute the effective action as well as the equation of motion.
Keywords
Cite
@article{arxiv.1302.1652,
title = {U-geometry : SL(5)},
author = {Jeong-Hyuck Park and Yoonji Suh},
journal= {arXiv preprint arXiv:1302.1652},
year = {2013}
}
Comments
1+26 pages, minor change, published version; v3 numerical errors in (5.8), (5.9) corrected