Four-dimensional N=4 SO(4) Gauged Supergravity from D=11

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

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Four-dimensional N=4 SO(4) Gauged Supergravity from D=11

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

High Energy Physics - Theory · Submitted 1 Nov 1999

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

The authors' main claim We construct the complete and explicit non-linear Kaluza-Klein Ansatz for deriving the bosonic sector of the standard N=4 SO(4) gauged four-dimensional supergravity from the reduction of D=11 supergravity on S^7.

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We construct the complete and explicit non-linear Kaluza-Klein Ansatz for deriving the bosonic sector of the standard N=4 SO(4) gauged four-dimensional supergravity from the reduction of D=11 supergravity on S^7. This provides a way of interpreting all bosonic solutions of the four-dimensional gauged theory as exact solutions in eleven-dimensional supergravity. We discuss certain limiting forms of the Kaluza-Klein reduction, and compare them with related forms in the Freedman-Schwarz N=4 SU(2)xSU(2) gauged theory. This leads us to the result that the Freedman-Schwarz model is in fact a singular limiting case of the standard SO(4) gauged supergravity. We show that in this limit, our Ansatz for getting the SO(4) gauged theory as an S^7 reduction from D=11 indeed reduces to an S^3 x S^3 reduction from D=10, which makes contact with previous results in the literature. We also show that there is no distinction to be made between having equal or unequal values for the gauge coupling constants $g$ and $\tilde g$ of the two SU(2) gauge-group factors in the standard N=4 SO(4) gauged supergravity, whilst by contrast the ratio of $g$ to $\tilde g$ is a non-trivial parameter of the Freedman-Schwarz model.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We construct the complete and explicit non-linear Kaluza-Klein Ansatz for deriving the bosonic sector of the standard N=4 SO(4) gauged four-dimensional supergravity from the reduction of D=11 supergravity on S^7.	contribution 1.00	0.97	0.52	asserted 1.00
s1	This provides a way of interpreting all bosonic solutions of the four-dimensional gauged theory as exact solutions in eleven-dimensional supergravity.	interpretation 0.99	0.74	0.20	asserted 0.79
s2	We discuss certain limiting forms of the Kaluza-Klein reduction, and compare them with related forms in the Freedman-Schwarz N=4 SU(2)xSU(2) gauged theory.	contribution 0.72	0.86	0.04	asserted 0.89
s3	This leads us to the result that the Freedman-Schwarz model is in fact a singular limiting case of the standard SO(4) gauged supergravity.	result 0.99	0.92	0.27	asserted 1.00
s4	We show that in this limit, our Ansatz for getting the SO(4) gauged theory as an S^7 reduction from D=11 indeed reduces to an S^3 x S^3 reduction from D=10, which makes contact with previous results in the literature.	result 0.93	0.94	0.10	asserted 1.00
s5	We also show that there is no distinction to be made between having equal or unequal values for the gauge coupling constants $g$ and $\tilde g$ of the two SU(2) gauge-group factors in the standard N=4 SO(4) gauged supergravity, whilst by contrast the ratio of $g$ to $\tilde g$ is a non-trivial parameter of the Freedman-Schwarz model.	result 1.00	0.92	0.13	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.91 · evidence from proof or derivation 1.00.

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Original abstract

We construct the complete and explicit non-linear Kaluza-Klein Ansatz for deriving the bosonic sector of the standard N=4 SO(4) gauged four-dimensional supergravity from the reduction of D=11 supergravity on S^7. This provides a way of interpreting all bosonic solutions of the four-dimensional gauged theory as exact solutions in eleven-dimensional supergravity. We discuss certain limiting forms of the Kaluza-Klein reduction, and compare them with related forms in the Freedman-Schwarz N=4 SU(2)xSU(2) gauged theory. This leads us to the result that the Freedman-Schwarz model is in fact a singular limiting case of the standard SO(4) gauged supergravity. We show that in this limit, our Ansatz for getting the SO(4) gauged theory as an S^7 reduction from D=11 indeed reduces to an S^3 x S^3 reduction from D=10, which makes contact with previous results in the literature. We also show that there is no distinction to be made between having equal or unequal values for the gauge coupling constants $g$ and $\tilde g$ of the two SU(2) gauge-group factors in the standard N=4 SO(4) gauged supergravity, whilst by contrast the ratio of $g$ to $\tilde g$ is a non-trivial parameter of the Freedman-Schwarz model.

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Cited by 12 Pith papers

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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.
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How the literature uses it

23 arXiv papers cite this in 45 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 · 23 sentences without a confident label

Builds on it 2 papers

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
In this appendix we show how to obtain the $N=4$ $Spin(4)$ gauged supergravity discussed in the bulk of the paper [ref] from the maximal $N=8$ $Spin(8)$ gauged supergravity [ref] , by extending the ansatz of [ref] to include fermions and gauge fields.

Boundary Conditions in Topological AdS$_4$/CFT$_3$ · Reduction from N=8 supergravity · 0.90

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
After uplifting our solutions on $S^7$ using [ref] we find [equation] where [equation] and the coordinate $ν$ with $0≤ν≤π/2$ parametrises the interval in the foliation of $S^7$ by the two $S^3$'s in the uplift.

Spatially modulated and supersymmetric deformations of ABJM theory · BPS equations · 0.94
The eleven-dimensional solution is a straight-forward application of the uplift formulae in [ref] and can be found in appendix [ref] (see also [ref] where the uplift was performed for a similar application).

Quantized Strings and Instantons in Holography · Single mass deformation of ABJ(M) · 0.94

Compares with it 2 papers

The bosonic action ([ref]) matches the one in [ref] [Fields are related by $χ_ [ref] = -χ_here$, $ϕ_ [ref] = ξ_here$, $A_ [ref] = √(2) A_here$ (for all vectors) and $g_ [ref] = g_here/√(2)$.] (see [ref] for original references).

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These findings reproduce the discussion of [ref] , where the $α=0$ case was also related to a singular limit of the $α=π/2$ one, corresponding to deforming $S^7$ into $S^3×S^3×S^1$.

Electric-magnetic deformations of D=4 gauged supergravities · Pure $=4$ (4) gauged supergravities · 0.80

Cites it as background 10 papers

A pioneering example was the truncation of 11D supergravity on $S^7$ down to the pure $𝒩=4$ $SO(4)_R$-gauged supergravity of [ref] worked out in [ref] .

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See also [ref] for previous construction of these 28-beins from the $N=4$ gauged $SO(4) =SU(2) ×SU(2)$ truncation of the full $N=8$ gauged $SO(8)$ theory.

N=8 Gauged Supergravity Theory and N=6 Superconformal Chern-Simons Matter Theory · The $28 ×28$ matrices $u$ and $v$, $A_2$ tensor, kinetic terms, and $SU(8)$ connection with $SO(4) ×SO(4)$ symmetry in $ · 0.82
$=4$ gauged supergravity in four-dimensions.— 4d $= 4$ $(4)$ gauged supergravity can be obtained as the consistent truncation of 11d supergravity on $S^7$ [ref] .

Universal AdS black holes in theories with sixteen supercharges and their microstates · Introduction · 0.83

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