Consistent Sphere Reductions and Universality of the Coulomb Branch in the Domain-Wall/QFT Correspondence

Details Consistent Sphere Reductions and Universality of the Coulomb Branch in the Domain-Wall/QFT Correspondence Consistent Sphere Reductions and Universality of the Coulomb Branch in the Domain-Wall/QFT Correspondence

2000-04-27

arxiv.org/abs/hep-th/0004201v2

Nucl.Phys.B590:213-232,2000

Physics

High Energy Physics

High Energy Physics - Theory

latex file, 21 pages, 1 figure, minor typo corrections

Scientific paper

10.1016/S0550-3213(00)00462-4

We prove that any D-dimensional theory comprising gravity, an antisymmetric n-index field strength and a dilaton can be consistently reduced on S^n 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 couping of the dilaton to the field strength is appropriately chosen. A consistent reduction can then be performed for n\le 5; with D being arbitrary when n\le 3, whilst D\le 11 for n=4 and D\le 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.

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