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Symmetries of Einstein-Yang-Mills fields and dimensional reduction

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Abstract

LetE be a manifold on which a compact Lie groupS acts simply (all orbits of the same type);E can be written locally asM×S/I,M being the manifold of orbits (space-time) andI a typical isotropy group for theS action. We study the geometrical structure given by anS-invariant metric and anS-invariant Yang Mills field onE with gauge groupR. We show that there is a one to one correspondence between such structures and quadruplets

of fields defined solely onM; γμv is a metric onM,h αβ are scalar fields characterizing the geometry of the orbits (internal spaces), Φ iα are other scalar fields (Higgs fields) characterizing theS invariance of the Lie(R)-valued Yang Mills field and

is a Yang Mills field for the gauge groupN(I)|I×Z(λ(I)),N(I) being the normalizer ofI inS, λ is a homomorphism ofI intoR associated to theS action, andZ(λ(I)) is the centralizer ofλ(I) inR. We express the Einstein-Yang-Mills Lagrangian ofE in terms of the component fields onM. Examples and model building recipes are given.

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Authors and Affiliations

  1. Centre de Physique Théorique, Section II, CNRS — Luminy — Case 907, F-13288, Marseille, Cedex 9, France

    R. Coquereaux & A. Jadczyk

  2. Institute of Theoretical Physics, University of Wroclaw, Poland

    R. Coquereaux & A. Jadczyk

  3. Laboratoire Propre, Centre National de la Recherche Scientifique, France

    A. Jadczyk

Authors
  1. R. Coquereaux
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  2. A. Jadczyk
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Communicated by G. Mack

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Coquereaux, R., Jadczyk, A. Symmetries of Einstein-Yang-Mills fields and dimensional reduction. Commun.Math. Phys. 98, 79–104 (1985). https://doi.org/10.1007/BF01211045

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