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Consistent Sphere Reductions and Universality of the Coulomb Branch in the Domain-Wall/QFT Correspondence
High Energy Physics - Theory · Submitted 27 Apr 2000
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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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 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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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. | result 0.81 | 0.93 | 0.80 | asserted 1.00 |
| s1 | 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. | result 0.81 | 0.82 | 0.13 | asserted 0.94 |
| s2 | (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. | contribution 0.52 | 0.92 | 0.09 | asserted 0.98 |
| s3 | 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. | result 0.73 | 0.96 | 0.18 | asserted 1.00 |
| s4 | 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. | result 0.90 | 0.96 | 0.17 | asserted 1.00 |
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Original 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 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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How the literature uses it
13 arXiv papers cite this in 20 sentences
Papers citing it · 13 sentences without a confident label
Cites it as background 6 papers
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A thorough survey of this literature would take us far afield, but in this paper we have drawn heavily upon [ref] .
Supersymmetry and Superstrata in Three Dimensions · Introduction · 0.86
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The relationship between $= (1,0)$ supergravity coupled to one anti-self-dual tensor multiplet in six dimensions and the three-dimensional $4$, $SO(4,4)$ supergravity (with $n=1$) has been laid out in [ref] .
Microstate Geometries from Gauged Supergravity in Three Dimensions · Some supergravity background · 0.80
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Generic consistent $S^3$ truncations in (super)gravity have been discussed in [ref] , where the full non-linear Kaluza-Klein Ansätze were constructed for a higher-dimensional theory that comprises the field content of the bosonic string.
Consistent $S^3$ reductions of six-dimensional supergravity · Introduction · 0.80
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