Non-Supersymmetric Attractor Flow in Symmetric Spaces
TL;DR: In this article, extremal black hole solutions for a variety of four dimensional models which admit a description in terms of 3D gravity coupled to a sigma model with symmetric target space were derived.
Abstract: We derive extremal black hole solutions for a variety of four dimensional models which, after Kaluza-Klein reduction, admit a description in terms of 3D gravity coupled to a sigma model with symmetric target space. The solutions are in correspondence with certain nilpotent generators of the isometry group. In particular, we provide the exact solution for a non-BPS black hole with generic charges and asymptotic moduli in N=2 supergravity coupled to one vector multiplet. Multi-centered solutions can also be generated with this technique. It is shown that the non-supersymmetric solutions lack the intricate moduli space of bound configurations that are typical of the supersymmetric case.
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TL;DR: In this paper, extremal, spherically symmetric black hole solutions to 4D supergravity with charge assignments that preclude BPS-saturation were constructed and the ground state energy as a function of charges and moduli was determined.
Abstract: We construct extremal, spherically symmetric black hole solutions to 4D supergravity with charge assignments that preclude BPS-saturation. In particular, we determine the ground state energy as a function of charges and moduli. We find that the mass of the non-BPS black hole remains that of a marginal bound state of four basic constituents throughout the entire moduli space and that there is always a non-zero gap above the BPS bound.
100 citations
Cites result from "Non-Supersymmetric Attractor Flow i..."
...While this paper was in preparation, some overlapping and complementary results appeared in [16]....
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TL;DR: In this article, the authors extend the discussion of the Kerr/CFT correspondence to the more general gauge/gravity correspondence in the full extremal black hole space-time of the bulk by using a technique of the holographic renormalization group (RG) flow.
Abstract: We extend the discussion of the 'Kerr/CFT correspondence' and its recent developments to the more general gauge/gravity correspondence in the full extremal black hole space-time of the bulk by using a technique of the holographic renormalization group (RG) flow. It is conjectured that the extremal black hole space-time is holographically dual to the chiral two-dimensional field theory. Our example is a typical four-dimensional Reissner-Nordstrom black hole, a system in which the M5-brane is wrapped on four cycles of Calabi-Yau threefold. In the five-dimensional supergravity viewpoint, this near horizon geometry is AdS{sub 3}xS{sup 2}, and three-dimensional gravity coupled to moduli fields is effectively obtained after a dimensional reduction on S{sup 2}. Constructing the Hamilton-Jacobi equation, we define the holographic RG flow from the three-dimensional gravity. The central charge of the Virasoro algebra is calculable from the conformal anomaly at the point where the beta function defined from the gravity side becomes zero. In general, we can also identify the c function of the dual two-dimensional field theory. We show that these flow equations are completely equivalent to not only BPS but also non-BPS attractor flow equations of the moduli fields. The attractor mechanism by which the values of the moduli fieldsmore » are fixed at the event horizon of the extremal black hole can be understood equivalently to the fact that the RG flows are fixed at the critical points in the dual field theory.« less
76 citations
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TL;DR: In this article, a pedagogical, introductory review of the so-called Attractor Mechanism (AM) at work in two different 4-dimensional frameworks: extremal black holes in N=2 supergravity and N=1 flux compactifications.
Abstract: These lectures provide a pedagogical, introductory review of the so-called Attractor Mechanism (AM) at work in two different 4-dimensional frameworks: extremal black holes in N=2 supergravity and N=1 flux compactifications. In the first case, AM determines the stabilization of scalars at the black hole event horizon purely in terms of the electric and magnetic charges, whereas in the second context the AM is responsible for the stabilization of the universal axion-dilaton and of the (complex structure) moduli purely in terms of the RR and NSNS fluxes. Two equivalent approaches to AM, namely the so-called ``criticality conditions'' and ``New Attractor'' ones, are analyzed in detail in both frameworks, whose analogies and differences are discussed. Also a stringy analysis of both frameworks (relying on Hodge-decomposition techniques) is performed, respectively considering Type IIB compactified on $CY_{3}$ and its orientifolded version, associated with $\frac{CY_{3}\times T^{2}}{\mathbb{Z}_{2}}$. Finally, recent results on the U-duality orbits and moduli spaces of non-BPS extremal black hole attractors in $3\leqslant N\leqslant 8$, d=4 supergravities are reported.
59 citations
TL;DR: In this paper, a class of non-supersymmetric multi-center solutions of the STU model of five-dimensional ungauged supergravity were derived by a system of linear equations defined on a four-dimensional Kahler manifold with vanishing Ricci scalar and a U(1) isometry.
Abstract: We find a class of non-supersymmetric multi-center solutions of the STU model of five-dimensional ungauged supergravity. The solutions are determined by a system of linear equations defined on a four-dimensional Kahler manifold with vanishing Ricci scalar and a U(1) isometry. The most general class of such Kahler manifolds was studied by LeBrun and they have non-trivial 2-cycles that can support the topological fluxes characteristic of bubbled geometries. After imposing an additional U(1) symmetry on the base we find explicit multi-center supergravity solutions. We show that there is an infinite number of regular multi-center solutions with non-trivial topology that are asymptotic to the near-horizon limit of a BMPV black hole.
44 citations
Cites background from "Non-Supersymmetric Attractor Flow i..."
...The construction of such solutions is a very important first step in understanding the structure and properties of non-BPS solutions in general, particularly since such solutions have played a pivotal role in the analysis of attractor flows [11, 12, 13, 14, 15, 16, 17], black-hole bound states, deconstruction [18, 19, 20], wall crossing and entropy enigmas [21, 22, 23]....
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TL;DR: The authors generalize Denef's method of deriving and solving first-order equations describing multicenter extremal black holes in four-dimensional N = 2 supergravity to allow non-supersymmetric solutions.
Abstract: Using the superpotential approach we generalize Denef's method of deriving and solving first-order equations describing multicenter extremal black holes in four-dimensional N = 2 supergravity to allow non-supersymmetric solutions. We illustrate the general results with an explicit example of the stu model.
34 citations
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TL;DR: In this paper, it was shown that explicit solutions can be constructed whenever an explicit formula is known in the theory at hand for the Bekenstein-hawking entropy of a single black hole as a function of its charges, and illustrate this with some simple examples.
Abstract: Four dimensional N=2 supergravity has regular, stationary, asymptotically flat BPS solutions with intrinsic angular momentum, describing bound states of separate extremal black holes with mutually nonlocal charges. Though the existence and some properties of these solutions were established some time ago, fully explicit analytic solutions were lacking thus far. In this note, we fill this gap. We show in general that explicit solutions can be constructed whenever an explicit formula is known in the theory at hand for the Bekenstein-Hawking entropy of a single black hole as a function of its charges, and illustrate this with some simple examples. We also give an example of moduli-dependent black hole entropy.
248 citations
TL;DR: In democratic STU-symmetric version, all three S and T and U duality symmetries are non-perturbative and mix electric and magnetic charges.
Abstract: We found double-extreme black holes associated with the special geometry of the Calabi-Yau moduli space with the prepotential F = STU. The area formula is STU-moduli independent and has [SL(2, Z)]{sup 3} symmetry in space of charges. The dual version of this theory without prepotential treats the dilaton S asymmetric versus T,U-moduli. We display the dual relation between new (STU) black holes and stringy (S|TU) black holes using particular Sp(8,Z) transformation. The area formula of one theory equals the area formula of the dual theory when expressed in terms of dual charges. We analyze the relation between (STU) black holes to string triality of black holes: (S|TU), (T|US), (U|ST) solutions. In democratic STU-symmetric version we find that all three S and T and U duality symmetries are non-perturbative and mix electric and magnetic charges.
241 citations
TL;DR: In this article, the authors exploit some common features of black hole and domain wall solutions of (super)gravity theories coupled to scalar fields and construct a class of stable extremal black holes that are non-BPS, but still can be described by first-order differential equations.
Abstract: We exploit some common features of black hole and domain wall solutions of (super)gravity theories coupled to scalar fields and construct a class of stable extremal black holes that are non-BPS, but still can be described by first-order differential equations. These are driven by a "superpotential'', which replaces the central charge Z in the usual black hole potential. We provide a general procedure for finding this class and deriving the associated "superpotential''. We also identify some other cases which do not belong to this class, but show a similar behaviour.
186 citations
TL;DR: The relation between the macroscopic entropy of four-dimensional BPS black holes and the microscopic counting of states, beyond the thermodynamical, large charge limit, was discussed in this paper.
Abstract: In these lecture notes, we review some recent developments on the relation between the macroscopic entropy of four-dimensional BPS black holes and the microscopic counting of states, beyond the thermodynamical, large charge limit. After a brief overview of charged black holes in supergravity and string theory, we give an extensive introduction to special and very special geometry, attractor flows and topological string theory, including holomorphic anomalies. We then expose the Ooguri-Strominger-Vafa (OSV) conjecture which relates microscopic degeneracies to the topological string amplitude, and review precision tests of this formula on ``small'' black holes. Finally, motivated by a holographic interpretation of the OSV conjecture, we give a systematic approach to the radial quantization of BPS black holes (i.e. quantum attractors). This suggests the existence of a one-parameter generalization of the topological string amplitude, and provides a general framework for constructing automorphic partition functions for black hole degeneracies in theories with sufficient degree of symmetry.
175 citations
TL;DR: In this paper, the entropy of extremal supersymmetric and non-supersymmetric black holes in N = 2 supergravity theories in four dimensions with higher derivative corrections is computed using the entropy function formalism.
Abstract: Using the entropy function formalism we compute the entropy of extremal supersymmetric and non-supersymmetric black holes in N=2 supergravity theories in four dimensions with higher derivative corrections. For supersymmetric black holes our results agree with all previous analysis. However in some examples where the four dimensional theory is expected to arise from the dimensional reduction of a five dimensional theory, there is an apparent disagreement between our results for non-supersymmetric black holes and those obtained by using the five dimensional description. This indicates that for these theories supersymmetrization of the curvature squared term in four dimension does not produce all the terms which would come from the dimensional reduction of a five dimensional action with curvature squared terms.
162 citations