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Ungauging black holes and hidden supercharges
High Energy Physics - Theory · Submitted 31 Oct 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Using this result, we show explicitly that some supersymmetries are preserved in the near horizon region of all the asymptotically flat solutions above, in the gauged theory.
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The abstract, sentence by sentence
We embed the general solution for non-BPS extremal asymptotically flat static and under-rotating black holes in abelian gauged D=4 N=2 supergravity, in the limit where the scalar potential vanishes but the gauging does not. Using this result, we show explicitly that some supersymmetries are preserved in the near horizon region of all the asymptotically flat solutions above, in the gauged theory. This reveals a deep relation between microscopic entropy counting of extremal black holes in Minkowski and BPS black holes in AdS. Finally, we discuss the relevance of this construction to the structure of asymptotically AdS4 black holes, as well as the possibility of including hypermultiplets.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We embed the general solution for non-BPS extremal asymptotically flat static and under-rotating black holes in abelian gauged D=4 N=2 supergravity, in the limit where the scalar potential vanishes but the gauging does not. | contribution 0.93 | 0.89 | 0.09 | asserted 0.98 |
| s1 | Using this result, we show explicitly that some supersymmetries are preserved in the near horizon region of all the asymptotically flat solutions above, in the gauged theory. | result 0.98 | 0.95 | 0.51 | asserted 1.00 |
| s2 | This reveals a deep relation between microscopic entropy counting of extremal black holes in Minkowski and BPS black holes in AdS. | interpretation 1.00 | 0.78 | 0.45 | asserted 0.99 |
| s3 | Finally, we discuss the relevance of this construction to the structure of asymptotically AdS4 black holes, as well as the possibility of including hypermultiplets. | future work 0.87 | 0.67 | 0.06 | hedged possibility 0.78 |
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The paper
Original abstract
We embed the general solution for non-BPS extremal asymptotically flat static and under-rotating black holes in abelian gauged D=4 N=2 supergravity, in the limit where the scalar potential vanishes but the gauging does not. Using this result, we show explicitly that some supersymmetries are preserved in the near horizon region of all the asymptotically flat solutions above, in the gauged theory. This reveals a deep relation between microscopic entropy counting of extremal black holes in Minkowski and BPS black holes in AdS. Finally, we discuss the relevance of this construction to the structure of asymptotically AdS4 black holes, as well as the possibility of including hypermultiplets.
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References
How the literature uses it
21 arXiv papers cite this in 42 sentences
Papers citing it · 37 sentences without a confident label
Uses its method or tool 1 paper
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Our strategy is to work with a symplectic completion of the BPS equations which results from electrically gauged models [ref] [see also [ref] where a similiar formalism has been used].
Supersymmetric Black Holes in AdS4 from Very Special Geometry · Introduction · 0.92
Cites it as background 4 papers
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This led e.g. to a symplectically covariant formulation of the equations satisfied by the solutions, of their attractor mechanism and scalar flow dynamics, as well as to the inclusion of coupling to hypermultiplets, cf. e.g. [ref] for an (incomplete) list of references.
Nonlinear symmetries of black hole entropy in gauged supergravity · Introduction · 0.96
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So far, much of the effort has been directed towards the analysis and characterization of black hole solutions of $𝒩=2$ Abelian Fayet-Iliopoulos gauged supergravity [ref] .
Black holes with halos · Introduction · 0.99
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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 · 141 sentences without a confident label
Builds on 3 papers
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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] .
Duality covariant non-BPS first order systems · Asymptotically flat solutions · 0.95
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Finally, we generalise this result in section [ref], where we show that the under-rotating attractors of all asymptotically flat black holes [ref] , again in the form described in [ref] , preserve two supercharges, i.e. they are $1/4$-BPS.
Rotating Attractors · Introduction · 0.84
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The scalar dependent inner product denoted by $(,)$ is a generalisation of [ref] in the rotating case that is explicitly given by [ref] [equation] for any two symplectic vectors of two-forms $𝒜$, $ℬ$, and we define $w=^2Uω$, as a shorthand below.
Supergravity flows and D-brane stability · Squaring of the action · 0.96
Uses the method or tool of 4 papers
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In order to study extremal solutions in abelian gauged supergravity with a flat potential, we consider the squaring of the action for such backgrounds [ref] , following closely the derivation of the known flow equations of [ref] for asymptotically AdS$_4$ black holes that preserve $1/4$ of the supersymmetries.
Supergravity flows and D-brane stability · Squaring of the action · 0.81
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In order to study extremal solutions in abelian gauged supergravity with a flat potential, we consider the squaring of the action for such backgrounds [ref] , following closely the derivation of the known flow equations of [ref] for asymptotically AdS$_4$ black holes that preserve $1/4$ of the supersymmetries.
Flow equations and attractors for black holes in N = 2 U(1) gauged supergravity · Squaring of the action · 0.81
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In order to integrate the flow equation [ref] above, one can follow the direct approach of [ref] , that leads to explicit solutions (see the example below).
Supersymmetric AdS_4 black holes and attractors · Asymptotically AdS$_4$ BPS black holes · 1.00
Compares with 9 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.].
Duality covariant non-BPS first order systems · Asymptotically flat solutions · 0.96
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The flow equations above are closely related to the ones obtained in [ref] for gauged supergravity, with the difference that the function $^ψ$ describing the spatial part of the metric is now fixed to $^ψ=r$ and that we have included the additional function $^φ$.
Flow equations and attractors for black holes in N = 2 U(1) gauged supergravity · Squaring of the action · 0.97
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Note that a Killing spinor satisfying this projection is rather different from the standard timelike Killing spinor projection that appears in asymptotically flat 1/2-BPS solutions (shown in [ref] below, see e.g. [ref] ), but is exactly the same as one of the projections appearing in asymptotically AdS$_4$ 1/4-BPS solutions (see [ref] ).
Stationary solutions of N=2 supergravity · Static attractors · 0.97
Cites as background 31 papers
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To a certain extent this analysis was carried out in section 8 of [ref] and will not be exhaustively repeated here.
Electric and magnetic charges in N=2 conformal supergravity theories · Analysis of the BPS conditions · 0.85
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More recently, the interest in four-dimensional black holes was extended to the more general case of asymptotically anti-de Sitter (AdS) spacetimes, described as solutions to gauged supergravity theories [ref] .
Supersymmetry of Anti-de Sitter Black Holes · Introduction · 0.96
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More recently, the interest in four-dimensional black holes was extended to the more general case of asymptotically anti-de Sitter (AdS) spacetimes, described as solutions to gauged supergravity theories [ref] .
Nonextremal black holes in gauged supergravity and the real formulation of special geometry · Introduction · 0.96
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