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Duality covariant non-BPS first order systems
High Energy Physics - Theory · Submitted 24 May 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim As an application, we directly solve these equations for the single-centre subclass, and write the general solution in a manifestly duality covariant form.
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The abstract, sentence by sentence
We study extremal black hole solutions to four dimensional N=2 supergravity based on a cubic symmetric scalar manifold. Using the coset construction available for these models, we define the first order flow equations implied by the corresponding nilpotency conditions on the three-dimensional scalar momenta for the composite non-BPS class of multi-centre black holes. As an application, we directly solve these equations for the single-centre subclass, and write the general solution in a manifestly duality covariant form. This includes all single-centre under-rotating non-BPS solutions, as well as their non-interacting multi-centre generalisations.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study extremal black hole solutions to four dimensional N=2 supergravity based on a cubic symmetric scalar manifold. | background 0.57 | 0.78 | 0.05 | asserted 0.96 |
| s1 | Using the coset construction available for these models, we define the first order flow equations implied by the corresponding nilpotency conditions on the three-dimensional scalar momenta for the composite non-BPS class of multi-centre black holes. | method 0.88 | 0.92 | 0.10 | asserted 1.00 |
| s2 | As an application, we directly solve these equations for the single-centre subclass, and write the general solution in a manifestly duality covariant form. | contribution 0.51 | 0.96 | 0.43 | asserted 1.00 |
| s3 | This includes all single-centre under-rotating non-BPS solutions, as well as their non-interacting multi-centre generalisations. | result 0.68 | 0.81 | 0.26 | asserted 1.00 |
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The paper
Original abstract
We study extremal black hole solutions to four dimensional N=2 supergravity based on a cubic symmetric scalar manifold. Using the coset construction available for these models, we define the first order flow equations implied by the corresponding nilpotency conditions on the three-dimensional scalar momenta for the composite non-BPS class of multi-centre black holes. As an application, we directly solve these equations for the single-centre subclass, and write the general solution in a manifestly duality covariant form. This includes all single-centre under-rotating non-BPS solutions, as well as their non-interacting multi-centre generalisations.
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References
How the literature uses it
19 arXiv papers cite this in 78 sentences
Papers citing it · 53 sentences without a confident label
Builds on it 1 paper
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The result is an extension of the static embedding of this section to the most general asymptotically flat extremal under-rotating black holes, as obtained in [ref] .
Ungauging black holes and hidden supercharges · Asymptotically flat solutions · 0.95
Uses its method or tool 1 paper
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To this end, we make use of the duality symmetries of the three-dimensional theory resulting from the dimensional reduction, through the formalism developed in [ref] .
Duality covariant multi-centre black hole systems · The $c^*$-map, nilpotent orbits and first order systems · 1.00
Compares with it 3 papers
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Indeed, the flow equations [ref] and [ref] with the particular solution for $φ$ given by [ref], can be straightforwardly shown to be identical to the static limit of the flow equations derived in [ref] for the single centre class of asymptotically flat black holes, upon identifying the gaugings $$ with the auxiliary vector $R̂^*$ used to express the solution[The interested reader can find an outline of this identification in appendix [ref], where the full rotating single center class is considered.].
Ungauging black holes and hidden supercharges · Asymptotically flat solutions · 0.96
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Note that in the single center class of [ref] these expressions were shown to vanish, consistent with the fact that $R̂^*$ is constant if the T-dualities are rigid.
Duality covariant multi-centre black hole systems · Connection to T-dualities · 0.90
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While this case was treated in detail in [ref] , we find it illuminating to solve the general equations in this case, since they are still nontrivial even though they lead to the same physical results as in a purely single-centre treatment.
non-BPS walls of marginal stability · Single centre flows · 0.81
Cites it as support 1 paper
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Indeed, we find that these vectors are determined by the electromagnetic charges $Γ$, up to duality transformations leaving $Γ$ invariant [ref] , so that they are determined in terms of $Γ$ and the asymptotic scalar fields $t^i_∞$.
Duality covariant multi-centre black hole systems · Overview of results · 0.96
Cites it as background 9 papers
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The composite non-BPS system [ref] describes the interactions of black holes that are non-BPS in isolation, while the almost-BPS system [ref] , allows for configurations of centres that are be both BPS and non-BPS in isolation.
Duality covariant multi-centre black hole systems · Introduction and overview · 0.90
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Beyond the supersymmetric sector, the non-BPS class of asymptotically flat black holes in supergravity has attracted attention, based on a deeper understanding of the first order systems underlying extremal static and under-rotating solutions (i.e. rotating black holes without an ergo-region) [ref] .
Ungauging black holes and hidden supercharges · Introduction · 0.87
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In section [ref] we look at the extremal under-rotating asymptotically flat black holes, which at two derivatives can be understood by alternative descriptions both in ungauged supergravity where supersymmetry is preserved only asymptotically [ref] , and in the so-called flat gauged supergravity where supersymmetry is preserved only at the horizon via twisting [ref] .
4d N=2 supergravity observables from Nekrasov-like partition functions · Organization of the rest of the paper · 0.91
What it cites · 38 sentences without a confident label
Builds on 2 papers
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In this section we generalise the formalism developed in [ref] to arbitrary nilpotent orbits of $G_3$, with a specific emphasis to the ones describing non-BPS black holes.
1/8 BPS black hole composites · Nilpotent orbits and first order systems · 1.00
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This formula [ref] generalises the rotating attractor formula derived in [ref] in specific duality frames.
Octonionic black holes · Physical properties · 0.93
Uses the method or tool of 1 paper
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Considering the asymptotic central charge $Z(Γ)_∞$ and its Kähler derivative $Z_a(Γ)_∞$ (which we will refer to as the `central charges' for simplicity), one can indeed define the asymptotic $Ω_a ∞$ as the unique solution of [ref] for which $α_∞$ is determined such that there is no NUT charge, [equation] as it is done in [ref] .
Octonionic black holes · Physical properties · 0.83
Compares with 7 papers
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This clearly reflects the situation one encounters in the known explicit solution defined through the almost-BPS system [ref] , and indeed one finds that [equation] where we defined the modified covariant derivative [equation] The form of this covariant derivative is exactly such that the corresponding composite connection is trivial by use of [ref], [ref] and [ref] [equation] It then follows that [ref] takes the form [equation] which implies that the vector fields are defined in terms of harmonic functions as [equation] such that for instance $⟨R̂^* , ⟩= - V$.
Non-BPS Black Rings and Black Holes in Taub-NUT · The linear system · 0.82
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This is quite different from the squaring of the action in the standard fake superpotential approach for single centre solutions [ref] , which is based on a function of scalars and physical charges only.
First order flows for N=2 extremal black holes and duality invariants · Conclusion · 0.99
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This is quite different from the squaring of the action in the standard fake superpotential approach for single centre solutions [ref] , which is based on a function of scalars and physical charges only.
Universality of the superpotential for d = 4 extremal black holes · Conclusion · 0.99
Cites as background 17 papers
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These are the standard BPS solutions [ref] , the so-called almost BPS solutions [ref] , and the composite non-BPS solutions [ref] .
Almost BPS black holes · Introduction and Overview · 0.94
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These are the standard BPS solutions [ref] , the so-called almost BPS solutions [ref] , and the composite non-BPS solutions [ref] .
Interacting non-BPS black holes · Introduction and Overview · 0.94
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The classification of extremal solutions in terms of nilpotent orbits has been studied in details in [ref] .
Black hole solutions to the $F_4$-model and their orbits (I) · Introduction and Overview · 0.88
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