Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-04-16
AnnalsPhys.323:2044-2072,2008
Physics
High Energy Physics
High Energy Physics - Theory
16 pages, no figures, references added
Scientific paper
10.1016/j.aop.2007.11.004
Many features of dimensional reduction schemes are determined by the breaking of higher dimensional general covariance associated with the selection of a particular subset of coordinates. By investigating residual covariance we introduce lower dimensional tensors --generalizing to one side Kaluza-Klein gauge fields and to the other side extrinsic curvature and torsion of embedded spaces-- fully characterizing the geometry of dimensional reduction. We obtain general formulas for the reduction of the main tensors and operators of Riemannian geometry. In particular, we provide what is probably the maximal possible generalization of Gauss, Codazzi and Ricci equations and various other standard formulas in Kaluza-Klein and embedded spacetimes theories. After general covariance breaking, part of the residual covariance is perceived by effective lower dimensional observers as an infinite dimensional gauge group. This reduces to finite dimensions in Kaluza-Klein and other few remarkable backgrounds, all characterized by the vanishing of appropriate lower dimensional tensors.
Maraner Paolo
Pachos Jiannis K.
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