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Compactification of d = 11 supergravity on S4 (or 11 = 7 + 4, too)
Authors:K. Pilch  P. van Nieuwenhuizen  P.K. Townsend
Affiliation:Institute for Theoretical Physics, State University of New York at Stony Brook, Stony Brook, Long Island, New York 11794, USA;Theory Group, Department of Physics, University of Texas at Austin, Austin, Texas, USA
Abstract:Eleven-dimensional supergravity can compactify spontaneously on either S7 or S4. We study the latter case, with attention to its connection with a possible gauged N = 4 supergravity in d = 7. We derive the linearized field equations and supersymmetry transformation rules for the effective d = 7 supergravity multiplet. There are five third rank antisymmetric tensors in this multiplet which are in the 5 representation of the gauge group USp(4) and they are propagated with a self-duality condition in 7 dimensions. There is also a 14 of scalar fields and they are found to propagate with a non-conformal wave operator.
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