Consistent sphere reductions and universality of the Coulomb branch in the domain-wall/QFT correspondence Original Research Article

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 n≤5; with D being arbitrary when n≤3, whilst D≤11 for n=4 and D≤10 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.