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arXiv · 1302.1652

U-geometry : SL(5)

Jeong-Hyuck Park·Yoonji Suh
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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.

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Jeong-Hyuck Park, Yoonji Suh. 2013-11-12. U-geometry : SL(5). https://doi.org/10.1007/jhep04(2013)147

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