Non-supersymmetric Black Holes Research Articles

Decay channels for double extremal black holes in four dimensions

We explore decay channels for charged black holes with vanishing temperature in \mathcal{N}=2𝒩=2 supersymmetric compactifications of string theory. If not protected by supersymmetry, such extremal black holes are expected to decay as a consequence of the weak gravity conjecture. We concentrate on double extremal, non-supersymmetric black holes for which the values of the scalar fields are constant throughout space-time, and explore decay channels for which decay into BPS and anti-BPS constituents is energetically favorable. We demonstrate the existence of decay channels at tree level for large families of double extremal black holes. For specific charges, we also find stable non-supersymmetric black holes, suggesting recombination of (anti)-supersymmetric constituents to a non-supersymmetric object.

Critical points of warped AdS/CFT and higher-curvature gravity

WAdS/WCFT correspondence is an interesting realization of non-AdS holography. It relates 3-dimensional Warped-Anti-de Sitter (WAdS$_3$) spaces to a special class of 2-dimensional quantum field theory with chiral scaling symmetry that acts only on right-moving modes. The latter are often called Warped Conformal Field Theories (WCFT$_2$), and their existence makes WAdS/WCFT particularly interesting as a tool to investigate a new type of 2-dimensional conformal structure. Besides, WAdS/WCFT is interesting because it enables to apply holographic techniques to the microstate counting problem of non-AdS, non-supersymmetric black holes. Asymptotically WAdS$_3$ black holes (WBH$_3$) appear as solutions of topologically massive theories, Chern-Simons theories, and many other models. Here, we explore WBH$_3\times \Sigma_{D-3}$ solutions of $D$-dimensional higher-curvature gravity, with $\Sigma_{D-3}$ being different internal manifolds, typically given by products of deformations of hyperbolic spaces, although we also consider warped products with time-dependent deformations. These geometries are solutions of the second order higher-curvature theory at special (critical) points of the parameter space, where the theory exhibits a sort of degeneracy. We argue that the dual (W)CFT at those points is actually trivial. In many respects, these critical points of WAdS$_3 \times \Sigma_{D-3}$ vacua are the squashed/stretched analogs of the AdS$_D$ Chern-Simons point of Lovelock gravity.

Non-supersymmetric black holes with α′ corrections

We study extremal 5- and 4-dimensional black hole solutions of the Heterotic Superstring effective action at first order in α′ with, respectively, 3 and 4 charges of arbitrary signs. For a particular choice of the relative signs of these charges the solutions are supersymmetric, but other signs give rise to non-supersymmetric extremal black holes. Although at zeroth order all these solutions are formally identical, we show that the α′ corrections are drastically different depending on how we break supersymmetry. We provide fully analytic mathcal{O} (α′) solutions and we compute their charges, masses and entropies and check that they are invariant under α′-corrected T-duality transformations. The masses of some of these black holes are corrected in a complicated way, but we show that the shift is always negative, in agreement with the Weak Gravity Conjecture. Our formula for the corrected entropy of the four-dimensional black holes generalizes previous results obtained from the entropy function method, as we consider a more general way in which supersymmetry can be broken.

Distributions of extremal black holes in Calabi-Yau compactifications

We study non-supersymmetric extremal black hole excitations of 4d mathcal{N} = 2 supersymmetric string vacua arising from compactification on Calabi-Yau threefolds. The values of the (vector multiplet) moduli at the black hole horizon are governed by the attractor mechanism. This raises natural questions, such as “what is the distribution of attractor points on moduli space?” and “how many attractor black holes are there with horizon area up to a certain size?” We employ tools developed by Denef and Douglas [1] to answer these questions.

Two kissing bolts

The study of non-supersymmetric black hole microstates offers the potential to resolve the black hole information paradox. A system of equations was recently obtained that enables the systematic construction of non-supersymmetric smooth horizonless supergravity solutions, that are candidates to describe microstates of non-extremal black holes. Within this system we construct a family of six-dimensional supergravity solutions that feature two topologically-nontrivial three-cycles known as bolts. The two bolts touch at a single point and are supported by fluxes. We find that the fluxes on the two three-cycles can be either aligned or anti-aligned, and exhibit examples of both. We present several examples of smooth solutions, including near-extremal solutions that have an approximate AdS3 region, and far-from extremal solutions that have arbitrarily small charge compared to their mass.

Non-renormalization for non-supersymmetric black holes

We analyze large logarithmic corrections to 4D black hole entropy and relate them to the Weyl anomaly. We use duality to show that counter-terms in EinsteinMaxwell theory can be expressed in terms of geometry alone, with no dependence on matter terms. We analyze the two known mathcal{N} = 2 supersymmetric invariants for various non-supersymmetric black holes and find that both reduce to the Euler invariant. The c-anomaly therefore vanishes in these theories and the coefficient of the large logarithms becomes topological. It is therefore independent of continuous black hole parameters, such as the mass, even far from extremality.

The resolution of an entropy puzzle for 4D non-BPS black holes

We show the equality between macroscopic and microscopic (statistical) black hole entropy for a class of four dimensional non-supersymmetric black holes in $$ \mathcal{N} $$ = 2 supergravity theory, up to the first subleading order in their charges. This solves a long standing entropy puzzle for this class of black holes. The macroscopic entropy has been computed in the presence of a newly derived higher-derivative supersymmetric invariant of [1], connected to the five dimensional supersymmetric Weyl squared Lagrangian. Microscopically, the crucial role in obtaining the equivalence is played by the anomalous gauge gravitational Chern-Simons term.

Holographic description of non-supersymmetric orbifolded D1-D5-P solutions

Non-supersymmetric black hole microstates are of great interest in the context of the black hole information paradox. We identify the holographic description of the general class of non-supersymmetric orbifolded D1-D5-P supergravity solutions found by Jejjala, Madden, Ross and Titchener. This class includes both completely smooth solutions and solutions with conical defects, and in the near-decoupling limit these solutions describe degrees of freedom in the cap region. The CFT description involves a general class of states obtained by fractional spectral flow in both left-moving and right-moving sectors, generalizing previous work which studied special cases in this class. We compute the massless scalar emission spectrum and emission rates in both gravity and CFT and find perfect agreement, thereby providing strong evidence for our proposed identification. We also investigate the physics of ergoregion emission as pair creation for these orbifolded solutions. Our results represent the largest class of non-supersymmetric black hole microstate geometries with identified CFT duals presently known.

Spherical Symmetric Dyonic Black Holes and Vacuum Geometries in 4 D N=1 Supergravity on Kähler-ricci Soliton

In this paper we consider several aspects of dyonic non-supersymmetric black holes in fourdimensional N = 1 supergravity coupled to chiral and vector multiplets. The scalar manifold can be considered as a one-parameter family of Kähler manifolds generated by a Kähler–Ricci flow equation. This setup implies that we have a family of dyonic non-supersymmetric black holes deformed with respect to the flow parameter related to the Kähler–Ricci soliton, which possibly controls the nature of black holes, such as their asymptotic and near horizon geometries. We mainly consider two types of black holes, namely a family of dyonic Reissner–Nordströmlike black holes and Bertotti–Robinson-like black holes where the scalars are freezing all over spacetime and at the horizon, respectively. In addition, the corresponding vacuum structures for such black holes are also discussed in the context of Morse–(Bott) theory. Finally, we give some simple CPn-models whose superpotential and gauge couplings have a linear form.

Supersymmetric charged clouds in AdS 5

We consider supersymmetric holographic flows that involve background gauge fields dual to chemical potentials in the boundary field theory. We use a consistent truncation of gauged N=8 supergravity in five dimensions and we give a complete analysis of the supersymmetry conditions for a large family of flows. We examine how the well-known supersymmetric flow between two fixed points is modified by the presence of the chemical potentials and this yields a new, completely smooth, solution that interpolates between two global AdS spaces of different radii and with different values of the chemical potential. We also examine some black-hole-like singular flows and a new non-supersymmetric black hole solution. We comment on the interpretation of our new solutions in terms of giant gravitons and discuss the implications of our work for finding black-hole solutions in AdS geometries.

Instanton corrected non-supersymmetric attractors

We discuss non-supersymmetric attractors with an instanton correction in Type IIA string theory compactified on a Calabi-Yau three-fold at large volume. For a stable non-supersymmetric black hole, the attractor point must minimize the effective black hole potential. We study the supersymmetric as well as non-supersymmetric attractors for the D0-D4 system with instanton corrections. We show that in simple models, like the STU model, the flat directions of the mass matrix can be lifted by a suitable choice of the instanton parameters.

Non-supersymmetric extremal RN-AdS black holes in $$ \mathcal{N} = 2 $$ gauged supergravity

We investigate extremal Reissner-Nordstrom-AdS black holes in four-dimensional N=2 abelian gauged supergravity. We find a new attractor equation which is not reduced to the one in the asymptotically flat spacetime. Focusing on so-called the T^3-model with a single neutral vector multiplet, we obtain non-supersymmetric extremal Reissner-Nordstrom-AdS black hole solutions with regular event horizon in the D0-D4 and the D2-D6 charge configurations. The negative cosmological constant emerges even without the Fayet-Iliopoulos parameters. Furthermore, we also argue the formal description of the non-supersymmetric black hole solutions of the T^3-model and the STU-model in generic configurations.

Five dimensional non-supersymmetric black holes and strings

We study non-supersymmetric solutions of five dimensional N=2 supergravity theories coupled to an arbitrary number of abelian vector multiplets. The solutions constructed can be considered as deformations of known supersymmetric black hole and string solutions. General constraints coming from the analysis of the equations of motion are derived. These represent explicit conditions on the charges of the black holes and strings. The constraints are analyzed for theories where the scalar manifolds are symmetric spaces and explicit solutions are constructed in cases where the prepotential of the theory factorizes into a linear and a quadratic term.

Large charge four-dimensional extremalN= 2 black holes withR2-terms

We consider N=2 supergravity in four dimensions with small R^2 curvature corrections. We construct large charge extremal supersymmetric and non-supersymmetric black hole solutions in all space, and analyze their thermodynamic properties.

PARTITION FUNCTION OF NON-SUPERSYMMETRIC BLACK HOLES IN THE SUPERGRAVITY LIMIT

In this paper, we propose a free energy for general non-supersymmetric black hole attractors (with vanishing D0-brane charge) arising in type IIA(B) superstrings on 3-fold Calabi–Yau, in the supergravity limit. This, by definition, differs from its counterpart BPS free energy by a factor of 4. Correspondingly, a mixed ensemble for these black holes is proposed.

Duality symmetry and the Cardy limit

We study supersymmetric and non-supersymmetric extremal black holes obtained in Type IIA string theory compactified on K3 ? T2, with duality group O(6,?22,?) ? SL(2,?). In the Cardy limit an internal circle combines with the AdS2 component in the near horizon geometry to give a BTZ black hole whose entropy is given by the Cardy formula. We study black holes carrying D0?D4 and D0?D6 brane charges. We find, both in the supersymmetric and non-supersymmetric cases, that a generic set of charges cannot be brought to the Cardy limit using the duality symmetries. In the non-supersymmetric case, unlike the supersymmetric one, we find that when the charges are large, a small fractional change in them always allows the charges to be taken to the Cardy limit. These results could lead to a microscopic determination of the entropy for extremal non-supersymmetric black holes, including rotating cases like the extreme Kerr black hole in four dimensions.

Non-supersymmetric black holes and topological strings

We study non-supersymmetric, extremal four-dimensional black holes which arise upon compactification of type II superstrings on Calabi–Yau (CY) threefolds. We propose a generalization of the Ooguri–Strominger–Vafa (OSV) conjecture for higher-derivative corrections to the non-supersymmetric black hole entropy, in terms of the one-parameter refinement of topological string introduced by Nekrasov. We also study the attractor mechanism for non-supersymmetric black holes and show how the inverse problem of fixing charges in terms of the attractor value of CY moduli can be explicitly solved.

Moduli stabilization, large-volume dS minimum without [formula omitted]-branes, (non-)supersymmetric black hole attractors and two-parameter Swiss cheese Calabi–Yau's

We consider two sets of issues in this paper. The first has to do with moduli stabilization, existence of “area codes” [A. Giryavets, New attractors and area codes, JHEP 0603 (2006) 020, hep-th/0511215] and the possibility of getting a non-supersymmetric dS minimum without the addition of D 3 ¯ -branes as in KKLT for type II flux compactifications. The second has to do with the “inverse problem” [K. Saraikin, C. Vafa, Non-supersymmetric black holes and topological strings, hep-th/0703214] and “fake superpotentials” [A. Ceresole, G. Dall'Agata, Flow equations for non-BPS extremal black holes, JHEP 0703 (2007) 110, hep-th/0702088] for extremal (non-)supersymmetric black holes in type II compactifications. We use (orientifold of) a “Swiss cheese” Calabi–Yau [J.P. Conlon, F. Quevedo, K. Suruliz, Large-volume flux compactifications: Moduli spectrum and D3/D7 soft supersymmetry breaking, JHEP 0508 (2005) 007, hep-th/0505076] expressed as a degree-18 hypersurface in WCP 4 [ 1 , 1 , 1 , 6 , 9 ] in the “large-volume-scenario” limit [V. Balasubramanian, P. Berglund, J.P. Conlon, F. Quevedo, Systematics of moduli stabilisation in Calabi–Yau flux compactifications, JHEP 0503 (2005) 007, hep-th/0502058]. The main result of our paper is that we show that by including non-perturbative α ′ and instanton corrections in the Kähler potential and superpotential [T.W. Grimm, Non-perturbative corrections and modularity in N = 1 type IIB compactifications, arXiv: 0705.3253 [hep-th]], it may be possible to obtain a large-volume non-supersymmetric dS minimum without the addition of anti-D3 branes a la KKLT. The chosen Calabi–Yau has been of relevance also from the point of other studies of Kähler moduli stabilization via non-perturbative instanton contributions [F. Denef, M.R. Douglas, B. Florea, Building a better racetrack, JHEP 0406 (2004) 034, hep-th/0404257] and non-supersymmetric AdS vacua (and their subsequent dS-uplifts) using ( α ′ ) 3 corrections to the Kähler potential [V. Balasubramanian, P. Berglund, J.P. Conlon, F. Quevedo, Systematics of moduli stabilisation in Calabi–Yau flux compactifications, JHEP 0503 (2005) 007, hep-th/0502058; K. Becker, M. Becker, M. Haack, J. Louis, Supersymmetry breaking and alpha'-corrections to flux induced potentials, JHEP 0206 (2002) 060, hep-th/0204254; A. Westphal, de Sitter string vacua from Kähler uplifting, JHEP 0703 (2007) 102, hep-th/0611332; V. Balasubramanian, P. Berglund, Stringy corrections to Kähler potentials, SUSY breaking, and the cosmological constant problem, JHEP 0411 (2004) 085, hep-th/0408054].

Higher-order corrections to mass-charge relation of extremal black holes

We investigate the hypothesis that the higher-derivative corrections always make extremal non-supersymmetric black holes lighter than the classical bound and self-repulsive. This hypothesis was recently formulated in the context of the so-called swampland program. One of our examples involves an extremal heterotic black hole in four dimensions. We also calculate the effect of general four-derivative terms in Maxwell-Einstein theories in D dimensions. The results are consistent with the conjecture.

First-order flow equations for extremal black holes in very special geometry

We construct interpolating solutions describing single-center static extremal non-supersymmetric black holes in four-dimensional N = 2 supergravity theories with cubic prepotentials. To this end, we derive and solve first-order flow equations for rotating electrically charged extremal black holes in a Taub-NUT geometry in five dimensions. We then use the connection between five- and four-dimensional extremal black holes to obtain four-dimensional flow equations and we give the corresponding solutions.