U-geometry : SL(5)

U-geometry : SL(5)

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 i...

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Veröffentlicht in:arXiv.org 2013-11
Hauptverfasser: Park, Jeong-Hyuck, Suh, Yoonji
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Differential geometry
Equations of motion
Geometry
M theory
Mathematics - Differential Geometry
Physics - High Energy Physics - Theory
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description 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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subjects Differential geometry
Equations of motion
Geometry
M theory
Mathematics - Differential Geometry
Physics - High Energy Physics - Theory
title U-geometry : SL(5)
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