Abstract
A field theory on a(d + n)-dimensional manifold in the presence of ann-dimensional isometry group spanningn-dimensional orbit spaces may be reduced to a field theory on ad-dimensional manifold. The field content of such reduced theories is completely worked out when the isometries may be non-Abelian and the resultant space may have torsion. The equations of motion of the dimensionally reduced theory are obtained directly from the higher-dimensional theory. The reduced theory is given in terms of the metric tensor, a set of scalar fields, and a set of antisymmetric tensor fields.
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Supported in part by the Department of Energy under Contract DE-AS-2-76ER02978 and in part by the National Science Foundation under Grant NSF Phy 83 134 10.
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Mansouri, F., Witten, L. Non-Abelian isometries of multidimensional universes. Found Phys 14, 1095–1106 (1984). https://doi.org/10.1007/BF01882491
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DOI: https://doi.org/10.1007/BF01882491