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Consistent 4-form fluxes for maximal supergravity
High Energy Physics - Theory · Submitted 28 Jul 2015
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In particular, the ansaetze directly yield the components of the 4-form field strength in terms of the scalars and vectors of the four-dimensional maximal gauged supergravity---in this way they provide an explicit uplift of all four-dimensional consistent truncations of D=11 supergravity.
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The abstract, sentence by sentence
We derive new ansaetze for the 4-form field strength of D=11 supergravity corresponding to uplifts of four-dimensional maximal gauged supergravity. In particular, the ansaetze directly yield the components of the 4-form field strength in terms of the scalars and vectors of the four-dimensional maximal gauged supergravity---in this way they provide an explicit uplift of all four-dimensional consistent truncations of D=11 supergravity. The new ansaetze provide a substantially simpler method for uplifting d=4 flows compared to the previously available method using the 3-form and 6-form potential ansaetze. The ansatz for the Freund-Rubin term allows us to conjecture a `master formula' for the latter in terms of the scalar potential of d=4 gauged supergravity and its first derivative. We also resolve a long-standing puzzle concerning the antisymmetry of the flux obtained from uplift ansaetze.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We derive new ansaetze for the 4-form field strength of D=11 supergravity corresponding to uplifts of four-dimensional maximal gauged supergravity. | contribution 0.99 | 0.97 | 0.41 | asserted 1.00 |
| s1 | In particular, the ansaetze directly yield the components of the 4-form field strength in terms of the scalars and vectors of the four-dimensional maximal gauged supergravity---in this way they provide an explicit uplift of all four-dimensional consistent truncations of D=11 supergravity. | contribution 0.44 | 0.91 | 0.58 | asserted 1.00 |
| s2 | The new ansaetze provide a substantially simpler method for uplifting d=4 flows compared to the previously available method using the 3-form and 6-form potential ansaetze. | contribution 0.44 | 0.80 | 0.13 | asserted 1.00 |
| s3 | The ansatz for the Freund-Rubin term allows us to conjecture a `master formula' for the latter in terms of the scalar potential of d=4 gauged supergravity and its first derivative. | result 0.51 | 0.87 | 0.11 | speculative 0.85 |
| s4 | We also resolve a long-standing puzzle concerning the antisymmetry of the flux obtained from uplift ansaetze. | result 0.55 | 0.93 | 0.08 | asserted 1.00 |
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The paper
Original abstract
We derive new ansaetze for the 4-form field strength of D=11 supergravity corresponding to uplifts of four-dimensional maximal gauged supergravity. In particular, the ansaetze directly yield the components of the 4-form field strength in terms of the scalars and vectors of the four-dimensional maximal gauged supergravity---in this way they provide an explicit uplift of all four-dimensional consistent truncations of D=11 supergravity. The new ansaetze provide a substantially simpler method for uplifting d=4 flows compared to the previously available method using the 3-form and 6-form potential ansaetze. The ansatz for the Freund-Rubin term allows us to conjecture a `master formula' for the latter in terms of the scalar potential of d=4 gauged supergravity and its first derivative. We also resolve a long-standing puzzle concerning the antisymmetry of the flux obtained from uplift ansaetze.
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References
How the literature uses it
15 arXiv papers cite this in 42 sentences
Papers citing it · 32 sentences without a confident label
Compares with it 3 papers
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[ref] , equation [ref].
The Embedding of Gauged STU Supergravity in Eleven Dimensions · Consistency of the other uplift formulae with the general uplift ansätze · 0.81
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The new direct Ansatz for $F^mnpq$ is also much more effective than this old method — in order to verify the SO(3)$×$SO(3) invariant solution of 11-dimensional supergravity, the index-raising of $F_mnpq$ was one of the hardest tasks [ref] .
Non-linear uplift Ans\"atze for the internal metric and the four-form field-strength of maximal supergravity · Conclusion · 0.80
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We shall discuss here only the cases of sphere reductions (collected in Table [ref]), where our formulae can be compared with known uplift results [ref] .
Consistent truncations from the geometry of sphere bundles · Introduction · 0.98
Cites it as background 5 papers
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In this section we summarise briefly the uplift ansätze for the full $N=8$ gauged $SO(8)$ supergravity [ref] .
The Embedding of Gauged STU Supergravity in Eleven Dimensions · Complete ansätze for $N=8$ gauged $SO(8)$ supergravity · 0.88
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It is known that 11d supergravity admits a consistent truncation on $S^7$ [ref] to 4d maximal 4d $SO(8)$ gauged supergravity [ref] .
Continuous symmetries and charge measurement of boundary operators in holography · Low-energy effective action · 0.96
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The corresponding consistent $S^7$ reduction ansatz was given in [ref] , although the complete and explicit ansatz for the reduction of the 3-form field was obtained later in [ref] .
Consistent Warped $\mathbb R\times T^{1,1}$ Reduction of Heterotic Supergravity · Introduction · 0.88
What it cites · 69 sentences without a confident label
Contests 1 paper
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The construction could not be completed there because only part of the generalised vielbein was known; furthermore, as shown much later in Ref. [ref] , the ansatz as given in Ref. [ref] yields a tensor that is not totally antisymmetric.
Consistent truncation of d = 11 supergravity on AdS_4 x S^7 · Introduction · contest 0.90
Uses the method or tool of 2 papers
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The GVPs, used in this paper, are found [ref] by expressing the 56-bein in a GL(7) decomposition (in terms of the components of the $D=11$ fields) and by packaging its derivative in terms of generalised connections.
Generalised geometry from the ground up · Introduction · 0.94
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However, these components are easily calculated using the 3-form ansatz [ref] .
Deformations of gauged SO(8) supergravity and supergravity in eleven dimensions · Ansätze for other components of the 4-form field strength · 0.93
Compares with 6 papers
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Note that this is not a consequence of the derivative index running over seven directions, but rather a consequence of working with a generalised non-metricity rather than torsion-free compatible connections [ref] , which are valued in the 56 even when the base space is not extended as in Ref. [ref] .
$E_{d(d)} \times \mathbb{R}^+$ Generalised Geometry, Connections and M theory · Generalised vielbein postulate · 0.81
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Note that this is not a consequence of the derivative index running over seven directions, but rather a consequence of working with a generalised non-metricity rather than torsion-free compatible connections [ref] , which are valued in the 56 even when the base space is not extended as in Ref. [ref] .
Supersymmetric E$_{7(7)}$ Exceptional Field Theory · Generalised vielbein postulate · 0.81
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The generalised connections in Ref. [ref] are nevertheless related [ref] to the generalised connections in Ref. [ref] ; as are the connections in exceptional field theory [ref] , where the emphasis is on connections that are expressed in terms of the 56-bein of exceptional field theory [ref] .
Exceptional Field Theory II: E$_{7(7)}$ · Generalised vielbein postulate · 0.88
Cites as support 3 papers
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However, given the non-trivial nature of the reduction on the one hand and the remarkably simple form of the ansätze on the other, they have been explicitly verified for a number of stationary points of the four-dimensional scalar potential including the SO(7)$^±$, G$_2$ and SU(4)$^-$ invariant solutions [ref] .
Consistent truncation of d = 11 supergravity on AdS_4 x S^7 · Preliminaries · 0.97
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However, given the non-trivial nature of the reduction on the one hand and the remarkably simple form of the ansätze on the other, they have been explicitly verified for a number of stationary points of the four-dimensional scalar potential including the SO(7)$^±$, G$_2$ and SU(4)$^-$ invariant solutions [ref] .
Testing the non-linear flux ansatz for maximal supergravity · Preliminaries · 0.97
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However, given the non-trivial nature of the reduction on the one hand and the remarkably simple form of the ansätze on the other, they have been explicitly verified for a number of stationary points of the four-dimensional scalar potential including the SO(7)$^±$, G$_2$ and SU(4)$^-$ invariant solutions [ref] .
Non-linear Kaluza-Klein theory for dual fields · Preliminaries · 0.97
Cites as background 3 papers
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Except that in this case the supersymmetry transformation of $A_μνm$ will correspond in four dimensions to the supersymmetry transformation of the 133 two-form fields, $A_μνα,$ in the tensor hierarchy (see Ref. [ref] ).
The maximal D=4 supergravities · Preliminaries · 0.85
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However, it turns out to be more convenient to have the 56-bein such that its E$_7(7)$ index is decomposed in an SL(8) basis: [See, for example, Ref. [ref] for more explanation.] [equation]
E7(7) symmetry in perturbatively quantised N=8 supergravity · The 56-bein $𝒱$ · 0.85
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Nevertheless, for convenience, we can add seven extra auxiliary vectors (see e.g. Ref. [ref] and references therein).
Generalised geometry from the ground up · Preliminaries · 0.83
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