Consistent Kaluza-Klein sphere reductions
By M. Cvetič, Hong Lu, C. Pope. 2000
232 citations recorded by the source corpus.
We study the circumstances under which a Kaluza-Klein reduction on an n-sphere, with a massless truncation that includes all the Yang-Mills fields of $\mathrm{SO}(n+1),$ can be consistent at the full non-linear level. We take as the starting point a theory comprising a p-form field strength and (possibly) a dilaton, coupled to gravity in the higher dimension D. We show that aside from the previously studied cases with $(D,p)=(11,4)$ and (10,5) (associated with the ${S}^{4}$ and ${S}^{7}$ reductions of $D=11$ supergravity, and the ${S}^{5}$ reduction of type IIB supergravity), the only other possibilities that allow consistent reductions are for $p=2,$ reduced on ${S}^{2},$ and for $p=3,$ reduced on ${S}^{3}$ or ${S}^{D\ensuremath{-}3}.$ We construct the fully non-linear Kaluza-Klein Ans\"atze in all these cases. In particular, we obtain $D=3,$ $N=8,$ $\mathrm{SO}(8)$ and $D=7,$ $N=2,$ $\mathrm{SO}(4)$ gauged supergravities from ${S}^{7}$ and ${S}^{3}$ reductions of $N=1$ supergravity in $D=10.$
Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/fe2cdd477b4b565236075b1445e904dedffe3656
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Citations in the corpus
- Consistent Kaluza-Klein truncations via exceptional field theory (2014, unknown): “Other consistent sphere reductions have been constructed in [12–14], including the compactification on AdS7 ˆ S4.”
- Gauged locally supersymmetric D=3 nonlinear sigma models (2003, methodology): “These include the compactifications on spheres [8, 9], compactifications with nontrivial fluxes [10, 11, 12, 13], as well as the theories whose existence has been inferred from computing the Kaluza-Klein spectra in the context of the adS-CFT correspondence [14, 15, 16, 17, 18].”
- Flux compactifications of string theory on twisted tori (2005, background): “An important feature is that both kinds of Scherk-Schwarz reductions allow consistent truncations [3, 4, 5, 6], in the sense that it is consistent with the full higher-dimensional field equations to set all the massive KaluzaKlein modes to zero while keeping a finite number of light or massless fiel”
- Compact and Noncompact Gauged Maximal Supergravities in Three Dimensions (2001, background): “serve the maximal supersymmetry. Another matter coupled theory with half maximal supersymmetry, obtained by compactifying the ten-dimensional N=1 supergravity on a seven-sphere, has been discussed in [12] (however, [12]deals only with the bosonic part of the Lagrangian). In a different vein, [13] co”
- Fivebranes wrapped on SLAG three-cycles and related geometry (2001, background): “However, these instanton effects are suppressed in the large N limit and might not be expected to survive in the supergravity approximation.”
- The statistical mechanics of near-BPS black holes (2020, methodology): “Without the inclusion of extra massless fields, this ansatz does not generally satisfy all the higher dimensional Einstein equations [90].”
- Supergravity duals of gauge theories from F(4) gauged supergravity in six dimensions (2001, methodology): “Now, we compactify the 9-dimensional theory on S(3) using the formulae in [29].”
- Fivebranes wrapped on associative three-cycles (2000, methodology): “Uplifting to D=10 using the formulae in [17, 18] we get”
- Consistent Kaluza-Klein reductions for general supersymmetric AdS solutions (2007, background): “For example, it is only in very special circumstances that there is a consistent KK reduction on a sphere (for further discussion see [1]).”
- Duality orbits of non‐geometric fluxes (2012, background): “ classied in table 6. Orbits 1 { 3: These gaugings are non-geometric for every 6= 0; for = 0, they correspond to coset reductions of heterotic string theory. See e.g. the S3 compactication in ref. [44] giving rise to the SO(4) gauging. This theory was previously obtained in ref. [45] as N= 2 truncat”
- The supergravity dual of a theory with dynamical supersymmetry breaking (2001, background): “The research of H.N. was supported in part by DOE grant DE-FG02-90ER40542.”
- Spheres, Generalised Parallelisability and Consistent Truncations (2014, methodology): “This has been shown explicitly for S7 [9], S4 [10] and S3 [12] and for a subsector of S5.[11,34] We will consider each example in turn, demonstrating how the generalised geometry encodes the embedding tensor and the scalar field ansatz for the consistent truncation.”