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BPS Black Hole Horizons in N=2 Gauged Supergravity
High Energy Physics - Theory · Submitted 6 Aug 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We work in a symplectically covariant formalism which allows for both electric and magnetic gauging parameters as well as dyonic background charges and obtain the general solution to the BPS equations for horizons of the form $AdS_2\times \Sigma_g$.
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The abstract, sentence by sentence
We study static BPS black hole horizons in four dimensional N=2 gauged supergravity coupled to $n_v$-vector multiplets and with an arbitrary cubic prepotential. We work in a symplectically covariant formalism which allows for both electric and magnetic gauging parameters as well as dyonic background charges and obtain the general solution to the BPS equations for horizons of the form $AdS_2\times \Sigma_g$. In particular this means we solve for the scalar fields as well as the metric of these black holes as a function of the gauging parameters and background charges. When the special Kahler manifold is a symmetric space, our solution is completely explicit and the entropy is related to the familiar quartic invariant. For more general models our solution is implicit up to a set of holomorphic quadratic equations. For particular models which have known embeddings in M-theory, we derive new horizon geometries with dyonic charges and numerically construct black hole solutions. These correspond to M2-branes wrapped on a Riemann surface in a local Calabi-Yau five-fold with internal spin.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study static BPS black hole horizons in four dimensional N=2 gauged supergravity coupled to $n_v$-vector multiplets and with an arbitrary cubic prepotential. | contribution 0.97 | 0.94 | 0.07 | asserted 0.91 |
| s1 | We work in a symplectically covariant formalism which allows for both electric and magnetic gauging parameters as well as dyonic background charges and obtain the general solution to the BPS equations for horizons of the form $AdS_2\times \Sigma_g$. | method 0.79 | 0.95 | 0.23 | asserted 1.00 |
| s2 | In particular this means we solve for the scalar fields as well as the metric of these black holes as a function of the gauging parameters and background charges. | result 0.53 | 0.95 | 0.20 | asserted 1.00 |
| s3 | When the special Kahler manifold is a symmetric space, our solution is completely explicit and the entropy is related to the familiar quartic invariant. | result 0.97 | 0.91 | 0.16 | asserted 1.00 |
| s4 | For more general models our solution is implicit up to a set of holomorphic quadratic equations. | result 0.59 | 0.93 | 0.13 | asserted 1.00 |
| s5 | For particular models which have known embeddings in M-theory, we derive new horizon geometries with dyonic charges and numerically construct black hole solutions. | contribution 0.53 | 0.95 | 0.12 | asserted 1.00 |
| s6 | These correspond to M2-branes wrapped on a Riemann surface in a local Calabi-Yau five-fold with internal spin. | interpretation 0.88 | 0.76 | 0.09 | asserted 1.00 |
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The paper
Original abstract
We study static BPS black hole horizons in four dimensional N=2 gauged supergravity coupled to $n_v$-vector multiplets and with an arbitrary cubic prepotential. We work in a symplectically covariant formalism which allows for both electric and magnetic gauging parameters as well as dyonic background charges and obtain the general solution to the BPS equations for horizons of the form $AdS_2\times \Sigma_g$. In particular this means we solve for the scalar fields as well as the metric of these black holes as a function of the gauging parameters and background charges. When the special Kahler manifold is a symmetric space, our solution is completely explicit and the entropy is related to the familiar quartic invariant. For more general models our solution is implicit up to a set of holomorphic quadratic equations. For particular models which have known embeddings in M-theory, we derive new horizon geometries with dyonic charges and numerically construct black hole solutions. These correspond to M2-branes wrapped on a Riemann surface in a local Calabi-Yau five-fold with internal spin.
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References
How the literature uses it
32 arXiv papers cite this in 72 sentences
Papers citing it · 46 sentences without a confident label
Contests it 1 paper
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In particular the method studying near-horizon geometries developed in [ref] for the case of symmetric special Kähler manifolds doesn't work in this case, since the model is neither symmetric nor homogeneous.
Supersymmetric objects in gauged supergravities · Gauging, $AdS$ Vacua and Near-Horizon Analysis · contest 0.77
Uses its method or tool 4 papers
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Following the procedure described in [ref] [The equations [ref] are based on [ref] , with some misprints corrected.], the BPS equations in the near-horizon limit [ref] provide a set of equations for the variables ${R_1,R_2,λ^i}$ as functions of the gaugings $g_0,g^i$ and the charges $p^0,q_i$.In particular, since $R_2$ is directly related to the black hole entropy $S$, this yields an expression for $S$ in terms of the gaugings and charges.
BPS black holes in a non-homogeneous deformation of the stu model of $N=2$, $D=4$ gauged supergravity · Dyonic Fayet-Iliopoulos gaugings and near-horizon analysis · 0.96
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Assuming that these conditions are satisfied we can use the results of [ref] to analyze regular horizon geometries.
Supersymmetric Black Holes in AdS4 from Very Special Geometry · $AdS_2×_g$: IR boundary conditions · 0.94
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The classification of horizon configurations can be performed by virtue of the attractor mechanism [ref] which fixes the values of the scalars at the horizon in terms of the vector charges.
BPS black hole horizons from massive IIA · Motivation and outlook · 0.80
Compares with it 6 papers
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For the STU-model in particular, this gives a five-dimensional solution space whereas the analysis of [ref] predicts that there should be a six-dimensional solution space.
Static BPS Black Holes in AdS4 with General Dyonic Charges · Introduction · 0.92
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We note that the $$ depends nontrivially on $q^u$ (as opposed to the constant gauge couplings in the FI-gauged supergravity studied in [ref] ) which must in turn be evaluated by solving KVzero and AdS2Sigeq5.
Abelian Hypermultiplet Gaugings and BPS Vacua in N = 2 Supergravity · BPS Black Hole Horizons: AdS2 x Sigma · 0.85
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One particular representative of our new solutions had been previously constructed numerically in [ref] .
AdS Black Holes from Duality in Gauged Supergravity · Conclusions · 0.83
Cites it as background 14 papers
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In particular, BPS black hole solutions in AdS$_4$ [ref] , have been the subject of considerable recent interest, starting with the first AdS$_4$ solution with a spherical horizon, obtained in [ref] , which was later expanded upon with the work of [ref] .
Static BPS black holes in U(1) gauged supergravity · Introduction · 0.95
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The full black hole solutions in such theories were first found in [ref] and further worked out in [ref] .
Higher derivative corrections to BPS black hole attractors in 4d gauged supergravity · AdS · 0.81
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The available magnetic black holes[Dyonic AdS black holes were constructed recently in [ref] .] can instead be BPS only in the static limit [ref] (with the exception of one hyperbolic rotating solution [ref] ) with nonconstant scalars, see also [ref] [See [ref] for black hole solutions of this type in theories with nontrivial hypermultiplets.].
Rotating black holes in 4d gauged supergravity · Introduction · 0.80
What it cites · 21 sentences without a confident label
Uses the method or tool of 2 papers
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In this work we follow the pragmatic approach of [ref] and work with a theory which is a straightforward symplectic completion of [ref] .
Flow equations and attractors for black holes in N = 2 U(1) gauged supergravity · Introduction · 0.96
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In this work we follow the pragmatic approach of [ref] and work with a theory which is a straightforward symplectic completion of [ref] .
General Matter Coupled N=2 Supergravity · Introduction · 0.96
Compares with 5 papers
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Furthermore this is different still from the notation in [ref] where the gauging parameters were denoted $=g^ g_$ and $=⟨,⟩$.
Flow equations and attractors for black holes in N = 2 U(1) gauged supergravity · Symplectic Invariant Equations · 0.96
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This provides an alternative derivation from that in [ref] for the explicit entropy of BPS black holes when the special Kähler manifold is a symmetric space.
Lectures on on Black Holes, Topological Strings and Quantum Attractors (2.0) · Revisiting Black Hole Horizons in Ungauged $=2$ Supergravity · 0.81
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Nonetheless we note that the key equations in [ref] are identical in form to PiEq but real instead of holomorphic.
Calabi-Yau Black Holes · Revisiting Black Hole Horizons in Ungauged $=2$ Supergravity · 0.99
Cites as background 14 papers
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In ungauged supergravity, black hole horizons in theories with a general cubic prepotential were first systematically studied by Shmakova [ref] where an implicit solution was provided up to set of $n_v$ real quadratic equations for $n_v$ variables.
Calabi-Yau Black Holes · Introduction · 0.90
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There has been some futher study of these CK solutions as well as related non-BPS $AdS_4$ black holes [ref] ] and can be interpreted in M-theory as M2-branes wrapped on Riemann surfaces [ref] .
Non-supersymmetric Extremal RN-AdS Black Holes in N=2 Gauged Supergravity · Introduction · 0.98
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There has been some futher study of these CK solutions as well as related non-BPS $AdS_4$ black holes [ref] ] and can be interpreted in M-theory as M2-branes wrapped on Riemann surfaces [ref] .
Flow equations and attractors for black holes in N = 2 U(1) gauged supergravity · Introduction · 0.98
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