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

DOI10.1016/S0550-3213(00)00462-4zbMATH Open1006.83044arXivhep-th/0004201OpenAlexW3101286575WikidataQ58665916 ScholiaQ58665916MaRDI QIDQ5933298

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Publication date: 14 May 2001

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Abstract: 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 nle 5; with D being arbitrary when nle 3, whilst Dle 11 for n=4 and Dle 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.

Full work available at URL: https://arxiv.org/abs/hep-th/0004201

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