Geometry of The Embedding of Supergravity Scalar Manifolds in D=11 and D=10

C.N. Pope; H. Lu; M. Cvetic

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Geometry of The Embedding of Supergravity Scalar Manifolds in D=11 and D=10

M. Cvetic, H. Lu, C.N. Pope

High Energy Physics - Theory · Submitted 14 Feb 2000

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We briefly discuss the use of these emdedding Ansatze for the lifting of solutions back to the higher dimension.

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arXiv IDhep-th/0002099 (version 2)

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CitationC.N. Pope, H. Lu, M. Cvetic. "Geometry of The Embedding of Supergravity Scalar Manifolds in D=11 and D=10." arXiv:hep-th/0002099 (2000). https://pith.science/paper/C545JG2D

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Several recent papers have made considerable progress in proving the existence of remarkable consistent Kaluza-Klein sphere reductions of D=10 and D=11 supergravities, to give gauged supergravities in lower dimensions. A proof of the consistency of the full gauged SO(8) reduction on S^7 from D=11 was given many years ago, but from a practical viewpoint a reduction to a smaller subset of the fields can be more manageable, for the purposes of lifting lower-dimensional solutions back to the higher dimension. The major complexity of the spherical reduction Ansatze comes from the spin-0 fields, and of these, it is the pseudoscalars that are the most difficult to handle. In this paper we address this problem in two cases. One arises in a truncation of SO(8) gauged supergravity in four dimensions to U(1)^4, where there are three pairs of dilatons and axions in the scalar sector. The other example involves the truncation of SO(6) gauged supergravity in D=5 to a subsector containing a scalar and a pseudoscalar field, with a potential that admits a second supersymmetric vacuum aside from the maximally-supersymmetric one. We briefly discuss the use of these emdedding Ansatze for the lifting of solutions back to the higher dimension.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Several recent papers have made considerable progress in proving the existence of remarkable consistent Kaluza-Klein sphere reductions of D=10 and D=11 supergravities, to give gauged supergravities in lower dimensions.	background 1.00	0.03	0.03	asserted 1.00
s1	A proof of the consistency of the full gauged SO(8) reduction on S^7 from D=11 was given many years ago, but from a practical viewpoint a reduction to a smaller subset of the fields can be more manageable, for the purposes of lifting lower-dimensional solutions back to the higher dimension.	background 0.99	0.05	0.04	asserted 0.97
s2	The major complexity of the spherical reduction Ansatze comes from the spin-0 fields, and of these, it is the pseudoscalars that are the most difficult to handle.	background 0.96	0.08	0.04	asserted 1.00
s3	In this paper we address this problem in two cases.	contribution 0.97	0.43	0.04	asserted 0.78
s4	One arises in a truncation of SO(8) gauged supergravity in four dimensions to U(1)^4, where there are three pairs of dilatons and axions in the scalar sector.	contribution 0.92	0.30	0.05	asserted 0.98
s5	The other example involves the truncation of SO(6) gauged supergravity in D=5 to a subsector containing a scalar and a pseudoscalar field, with a potential that admits a second supersymmetric vacuum aside from the maximally-supersymmetric one.	contribution 0.98	0.49	0.06	asserted 1.00
s6	We briefly discuss the use of these emdedding Ansatze for the lifting of solutions back to the higher dimension.	contribution 0.56	0.66	0.07	asserted 0.54

What kind of paper the classifier reports this is: theoretical result 0.79 · evidence from proof or derivation 0.92.

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The paper

Original abstract

Several recent papers have made considerable progress in proving the existence of remarkable consistent Kaluza-Klein sphere reductions of D=10 and D=11 supergravities, to give gauged supergravities in lower dimensions. A proof of the consistency of the full gauged SO(8) reduction on S^7 from D=11 was given many years ago, but from a practical viewpoint a reduction to a smaller subset of the fields can be more manageable, for the purposes of lifting lower-dimensional solutions back to the higher dimension. The major complexity of the spherical reduction Ansatze comes from the spin-0 fields, and of these, it is the pseudoscalars that are the most difficult to handle. In this paper we address this problem in two cases. One arises in a truncation of SO(8) gauged supergravity in four dimensions to U(1)^4, where there are three pairs of dilatons and axions in the scalar sector. The other example involves the truncation of SO(6) gauged supergravity in D=5 to a subsector containing a scalar and a pseudoscalar field, with a potential that admits a second supersymmetric vacuum aside from the maximally-supersymmetric one. We briefly discuss the use of these emdedding Ansatze for the lifting of solutions back to the higher dimension.

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References

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Consistent truncation of d = 11 supergravity on AdS_4 x S^7
hep-th 2011-12 conditional novelty 7.0 of 10

The 1987 de Wit-Nicolai consistency conditions admit a larger solution space than assumed, and the eleven-dimensional fluxes are invariant under that extra freedom, which completes the proof of the S^7 truncation.
N=2 Supersymmetric RG Flows and the IIB Dilaton
hep-th 2000-04 conditional novelty 7.0 of 10

The IIB dilaton and axion are argued, by conjecture plus a full ten-dimensional consistency check, to be a nontrivial function of the five-dimensional E6(6) scalar matrix rather than its SL(2,R) factor alone.
Consistent SO(6) Reduction Of Type IIB Supergravity on S^5
hep-th 2000-03 conditional novelty 7.0 of 10

The paper constructs the complete non-linear Kaluza-Klein reduction Ansatz for type IIB supergravity on a five-sphere, yielding five-dimensional gravity coupled to fifteen SO(6) gauge fields and twenty SL(6,R)/SO(6) s...
An N = 2 Supersymmetric Membrane Flow
hep-th 2001-07 accept novelty 6.0 of 10

An explicit M-theory solution is constructed and verified as the holographic dual of a supersymmetric mass flow in the (2+1)-dimensional M2-brane theory, with a generalization to conifold geometries.
Hodge Duals in Spherical Compactifications
hep-th 2025-07 conditional novelty 2.0 of 10

The paper obtains a closed-form expression for the constrained Hodge dual of a p-form under the spherical constraint x_i x_i = 1, which reduces to the standard hypersurface Hodge star with unit normal.

How the literature uses it

11 arXiv papers cite this in 31 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 22 sentences without a confident label

Builds on it 1 paper

Moreover, our derivation clarifies longstanding technical issues encountered in consistent Kaluza-Klein reductions on spheres and offers a general formalism that complements and extends the results found in prior literature such as [ref] .

Hodge Duals in Spherical Compactifications · Conclusion · 0.93

Uses its method or tool 3 papers

We can uplift the $D=4$ Susy Q-lattice solutions to $D=11$ either using the formulae for solutions of the $𝒩=2$ STU model in [ref] or the formulae for the $𝒩=4$ $SO(4)$ gauged supergravity model in [ref] .

Susy Q and spatially modulated deformations of ABJM theory · Supersymmetric boomerang solutions in $D=11$ · 0.98
Using the formula given in [ref] , any solution of the $N=2$ theory can be explicitly uplifted on a seven sphere to obtain an exact solution of $D=11$ supergravity.

Boomerang RG flows in M-theory with intermediate scaling · The set-up · 0.97
The uplift formula was constructed in [ref] , and we review it by following section 5 of [ref] .

A gravity interpretation for the complex Euclidean saddles of the ABJM index · Uplifting gauged STU supergravity to eleven dimensions · 0.87

Uses its data or values 1 paper

[ref] , which we reproduce here for convenience F̂_(4) = -2g U ϵ_ + F̂'_(4) + F̂”_(4) + Ĝ_ ,

The Embedding of Gauged STU Supergravity in Eleven Dimensions · Uplifting gauged STU supergravity to eleven dimensions · 0.91

Compares with it 1 paper

[ref] as follows

The Embedding of Gauged STU Supergravity in Eleven Dimensions · Derivation of $A_mnp$ · 0.87

Cites it as background 3 papers

Let us consider $U(1)^4$-gauged $𝒩=2$ supergravity in four dimensions, [ref] and [ref] .

A gravity interpretation for the complex Euclidean saddles of the ABJM index · Uplifting gauged STU supergravity to eleven dimensions · 0.85
Let us also mention that there exist partial results and uplift formulae for truncated versions of the maximal theory where the scalar sector is much simpler (see for example [ref] and references therein).

Testing the non-linear flux ansatz for maximal supergravity · Introduction · 0.87
There is a further consistent truncation of the latter to an $𝒩=2$, $U(1)^4$, gauged supergravity coupled to three vector multiplets, called the STU model [ref] .

Susy Q and spatially modulated deformations of ABJM theory · Consistent truncations of $D=11$ supergravity · 0.81

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