Consistent sphere reductions and universality of the Coulomb branch in the domain-wall/QFT correspondence
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We prove that any D-dimensional theory comprising gravity, an antisymmetric n-index field strength and a dilaton can be consistently reduced on Sn in a truncation in which just n scalar fields and the metric are retained in (D-n)-dimensions, provided only that the strength of the coupling of the dilaton to the field strength is appropriately chosen. A consistent reduction can then be performed for n5; with D being arbitrary when n3, whilst D11 for n=4 and D10 for n=5. (Or, by Hodge dualisation, n can be replaced by (D-n) in these conditions.) We obtain the lower-dimensional scalar potentials and construct associated domain wall solutions. We use the consistent reduction ansatz to lift domain-wall solutions in the (D-n)-dimensional theory back to D dimensions, where we show that they become certain continuous distributions of (D-n-2)-branes. We also examine the spectrum for a minimally-coupled scalar field in the domain-wall background, showing that it has a universal structure characterised completely by the dimension n of the compactifying sphere. 2000 Elsevier Science B.V.
