University of supersymmetric attractors

Journal of High Energy Physics, 2007

We analyze higher derivative corrections to attractor geometries in five dimensions. We find corrected AdS_3xS^2 geometries by solving the equations of motion coming from a recently constructed four-derivative supergravity action in five dimensions. The result allows us to explicitly verify a previous anomaly based derivation of the AdS_3 central charges of this theory. Also, by dimensional reduction we compare our results with those of the 4D higher derivative attractor, and find complete agreement.

Journal of High Energy Physics, 2007

The entropy and the attractor equations for static extremal black hole solutions follow from a variational principle based on an entropy function. In the general case such an entropy function can be derived from the reduced action evaluated in a near-horizon geometry. BPS black holes constitute special solutions of this variational principle, but they can also be derived directly from a different entropy function based on supersymmetry enhancement at the horizon. Both functions are consistent with electric/magnetic duality and for BPS black holes their corresponding OSV-type integrals give identical results at the semi-classical level. We clarify the relation between the two entropy functions and the corresponding attractor equations for N=2 supergravity theories with higher-derivative couplings in four space-time dimensions. We discuss how non-holomorphic corrections will modify these entropy functions.

Nuclear Physics B, 2001

We construct four-dimensional domain wall solutions of gauged supergravity coupled to vector and to hypermultiplets. The gauged supergravity theories that we consider are obtained by performing two types of Abelian gauging. In both cases we find that the behaviour of the scalar fields belonging to the vector multiplets is governed by the so-called attractor equations known from the study of BPS black hole solutions in ungauged supergravity theories. The scalar fields belonging to the hypermultiplets, on the other hand, are either constant or exhibit a run-away behaviour. These domain wall solutions preserve 1/2 of supersymmetry and they are, in general, curved. We briefly comment on the amount of supersymmetry preserved by domain wall solutions in gauged supergravity theories obtained by more general gaugings.

Journal of High Energy Physics, 2007

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.

Journal of High Energy Physics, 2007

We use the relation between extremal black hole solutions in five-and in fourdimensional N = 2 supergravity theories with cubic prepotentials to define the entropy function for extremal black holes with one angular momentum in five dimensions. We construct two types of solutions to the associated attractor equations.

Classical and Quantum Gravity, 2000

Modifications of the Bekenstein-Hawking area law for black holes are crucial in order to find agreement between the microscopic entropy based on state counting and the macroscopic entropy based on an effective field theory computation. We discuss this and related issues for the case of four-dimensional N=2 supersymmetric black holes. We also briefly comment on the state counting for N=4 and N=8 black holes.

Journal of High Energy Physics, 2006

At the horizon, a static extremal black hole solution in N=2 supergravity in four dimensions is determined by a set of so-called attractor equations which, in the absence of higher-curvature interactions, can be derived as extremization conditions for the black hole potential or, equivalently, for the entropy function. We contrast both methods by explicitly solving the attractor equations for a one-modulus prepotential associated with the conifold. We find that near the conifold point, the non-supersymmetric solution has a substantially different behavior than the supersymmetric solution. We analyze the stability of the solutions and the extrema of the resulting entropy as a function of the modulus. For the non-BPS solution the region of attractivity and the maximum of the entropy do not coincide with the conifold point.

Journal of High Energy Physics, 2007

We show that the second order field equations characterizing extremal solutions for spherically symmetric, stationary black holes are in fact implied by a system of first order equations given in terms of a prepotential W . This confirms and generalizes the results in . Moreover we prove that the squared prepotential function shares the same properties of a c-function and that it interpolates between M 2 ADM and M 2 BR , the parameter of the near-horizon Bertotti-Robinson geometry. When the black holes are solutions of extended supergravities we are able to find an explicit expression for the prepotentials, valid at any radial distance from the horizon, which reproduces all the attractors of the four dimensional N > 2 theories. Far from the horizon, however, for N -even our ansatz poses a constraint on one of the U-duality invariants for the non-BPS solutions with Z = 0. We discuss a possible extension of our considerations to the non extremal case. 1

Journal of High Energy Physics, 2007

We study the attractor mechanism for N = 1 supergravity coupled to vector and chiral multiplets and compute the attractor equations of these theories. These equations may have solutions depending on the choice of the holomorphic symmetric matrix f ΛΣ which appears in the kinetic lagrangian of the vector sector. Models with non trivial electric-magnetic duality group which have or have not attractor behavior are exhibited. For a particular class of models, based on an N = 1 reduction of homogeneous special geometries, the attractor equations are related to the theory of pure spinors.

Classical and Quantum Gravity, 2007

We express the d = 4, N = 2 black hole effective potential for cubic holomorphic F functions and generic dyonic charges in terms of d = 5 real special geometry data. The 4d critical points are computed from the 5d ones, and their relation is elucidated. For symmetric spaces, we identify the BPS and non-BPS classes of attractors and the respective entropies. These always derive from simple interpolating formulae between four and five dimensions, depending on the volume modulus and on the 4d magnetic (or electric) charges.

International Journal of Modern Physics A, 2006

We study the critical points of the black hole scalar potential V BH in N = 2, d = 4 supergravity coupled to n V vector multiplets, in an asymptotically flat extremal black hole background described by a 2 (n V + 1)-dimensional dyonic charge vector and (complex) scalar fields which are coordinates of a special Kähler manifold.

Physical Review D, 1997

Geometric Killing spinors which exist on AdS p+2 S d p 2 sometimes may be identied with supersymmetric Killing spinors. This explains the enhancement of unbroken supersymmetry near the p-brane horizon in d dimensions. The corresponding p-brane interpolates between two maximally supersymmetric vacua, at innity and at the horizon. New case is studied here: p = 0, d = 5. The details of supersymmetric version of the very special geometry are presented. We nd the area-entropy formula of the supersymmetric 5d black holes via the volume of S 3 which depends on charges and intersection matrix. 1

Physical Review D, 2006

We derive and solve the black hole attractor conditions of N = 8 supergravity by finding the critical points of the corresponding black hole potential. This is achieved by a simple generalization of the symplectic structure of the special geometry to all extended supergravities with N > 2. There are two classes of solutions for regular black holes, one for 1/8 BPS ones and one for the non-BPS. We discuss the solutions of the moduli at the horizon for BPS attractors using N = 2 language. An interpretation of some of these results in N = 2, STU black hole context helps to clarify the general features of the black hole attractors.

Physical Review D, 2009

We apply the entropy formalism to the study of the near-horizon geometry of extremal black p-brane intersections in D > 5 dimensional supergravities.

Physical Review D, 2010

Physical Review D, 2008

We consider extremal black hole attractors (both BPS and non-BPS) for N = 3 and N = 5 supergravity in d = 4 space-time dimensions.

Physical Review D, 2009

We consider the Bekenstein-Hawking entropy-area formula in four dimensional extended ungauged supergravity and its electric-magnetic duality property.

Physical Review D, 2008

The motion of a particle near the Reissner-Nordström black hole horizon is described by conformal mechanics. In this paper we present an extended one-dimensional analysis of the N = 4 superconformal mechanics coupled to n-copies of N = 8, d = 1 vector supermultiplets. The constructed system possesses a special Kähler geometry in the scalar sector of the vector multiplets as well as an N = 4 superconformal symmetry which is provided by a proper coupling to a dilaton superfield. The superconformal symmetry completely fixes the resulting action. We explicitly demonstrate that the electric and magnetic charges, presenting in the "effective black hole" action, appear as a result of resolving constraints on the auxiliary components of the vector supermultiplets. We present the component action, supercharges and Hamiltonian with all fermionic terms included. One of the possible ways to generalize the black hole potential is to consider a modified version of the N = 4 superconformal multiplet where its auxiliary components acquire non-zero constant values. We explicitly write down the corresponding modified black hole potential.

Journal of Mathematical Physics, 2011

We classify 2-center extremal black hole charge configurations through duality-invariant homogeneous polynomials, which are the generalization of the unique invariant quartic polynomial for single-center black holes based on homogeneous symmetric cubic special Kähler geometries.

Physical Review D, 2008

We generalize the description of the d = 4 Attractor Mechanism based on an effective black hole (BH) potential to the presence of a gauging which does not modify the derivatives of the scalars and does not involve hypermultiplets. The obtained results do not rely necessarily on supersymmetry, and they can be extended to d > 4, as well.

Journal of High Energy Physics, 2002

In this paper we present a classification of possible dynamics of closed string moduli within specific toroidal compactifications of Type II string theories due to the NS-NS tadpole terms in the reduced action. They appear as potential terms for the moduli when supersymmetry is broken due to the presence of D-branes. We particularise to specific constructions with two, four and six-dimensional tori, and study the stabilisation of the complex structure moduli at the disk level. We find that, depending on the cycle on the compact space where the brane is wrapped, there are three possible cases: i) there is a solution inside the complex structure moduli space, and the configuration is stable at the critical point, ii) the moduli fields are driven towards the boundary of the moduli space, iii) there is no stable solution at the minimum of the potential and the system decays into a set of branes.

Classical and Quantum Gravity, 1999

We present fivedimensional extreme black hole solutions of M-theory compactified on Calabi-Yau threefolds and study these solutions in the context of flop transitions in the extended Kähler cone. In particular we consider a specific model and present black hole solutions, breaking half of N = 2 supersymmetry, in two regions of the extended Kähler cone, which are connected by a flop transition. The conditions necessary to match both solutions at the flop transition are analysed. Finally we also discuss the conditions to obtain massless black holes at the flop transition.

Physical Review D - Particles, Fields, Gravitation and Cosmology, 2008

We present two generic classes of supersymmetric solutions of N = 2, d = 4 supergravity coupled to non-Abelian vector supermultiplets with a gauge group that includes an SU (2) factor. The first class consists of embeddings of the 't Hooft-Polyakov monopole and in the examples considered it has a fully regular, asymptotically flat space-time metric without event horizons. The other class of solutions consists of regular non-Abelian extreme black holes. There is a covariant attractor at the horizon of these non-Abelian black holes. 1 in Ref.

Journal of Mathematical Physics, 2001

We study supersymmetric domain walls on S 1 /Z 2 orbifolds. The supergravity solutions in the bulk are given by the attractor equation associated with Calabi-Yau spaces and have a naked space-time singularity at some |y s |. We are looking for possibilities to cut off this singularity with the second wall by a stringy mechanism. We use the collapse of the CY cycle at |y c | which happens before and at a finite distance from the space-time singularity. In our example with three Kähler moduli the second wall is at the end of the moduli space at |y c | where also the enhancement of SU (2) gauge symmetry takes place so that |y e | = |y c | < |y s |. The physics of the excision of a naked singularity via the enhançon in the context of domain wall has an interpretation on the heterotic side related to R → 1/R duality. The position of the enhançon is given by the equation R(|y e |) = 1.

Physical Review D, 2009

It is shown that the E 6(6) symmetric entropy formula describing black holes and black strings in D = 5 is intimately tied to the geometry of the generalized quadrangle GQ(2, 4) with automorphism group the Weyl group W (E 6 ). The 27 charges correspond to the points and the 45 terms in the entropy formula to the lines of GQ(2, 4). Different truncations with 15, 11 and 9 charges are represented by three distinguished subconfigurations of GQ(2, 4), well-known to finite geometers; these are the "doily" (i. e. GQ(2, 2)) with 15, the "perp-set" of a point with 11, and the "grid" (i. e. GQ(2, 1)) with 9 points, respectively. In order to obtain the correct signs for the terms in the entropy formula, we use a non-commutative labelling for the points of GQ(2, 4). For the 40 different possible truncations with 9 charges this labelling yields 120 Mermin squares -objects well-known from studies concerning Bell-Kochen-Specker-like theorems. These results are connected to our previous ones obtained for the E 7(7) symmetric entropy formula in D = 4 by observing that the structure of GQ(2, 4) is linked to a particular kind of geometric hyperplane of the split Cayley hexagon of order two, featuring 27 points located on 9 pairwise disjoint lines (a distance-3-spread). We conjecture that the different possibilities of describing the D = 5 entropy formula using Jordan algebras, qubits and/or qutrits correspond to employing different coordinates for an underlying non-commutative geometric structure based on GQ(2, 4).

Physical Review D, 1999

We consider general properties of central charges of zero-branes and associated duality invariants, in view of their double role, on the bulk and on the world volume (quantum mechanical) theory.

Fortschritte der Physik, 2014

We analyze the polynomial part of the Iwasawa realization of the coset representative of non compact symmetric Riemannian spaces. We start by studying the role of Kostant's principal SU (2) P subalgebra of simple Lie algebras, and how it determines the structure of the nilpotent subalgebras. This allows us to compute the maximal degree of the polynomials for all faithful representations of Lie algebras. In particular the metric coefficients are related to the scalar kinetic terms while the representation of electric and magnetic charges is related to the coupling of scalars to vector field strengths as they appear in the Lagrangian.

International Journal of Modern Physics A, 2010

We compute the effective black hole potential V BH of the most general N = 2,d = 4 (local ) special Kähler geometry with quantum perturbative corrections, consistent with axion-shift Peccei-Quinn symmetry and with cubic leading order behavior.

Journal of Mathematical Physics, 2011

We reconsider the sub-leading quantum perturbative corrections to N = 2 cubic special Kähler geometries. Imposing the invariance under axion-shifts, all such corrections (but the imaginary constant one) can be introduced or removed through suitable, lower unitriangular symplectic transformations, dubbed Peccei-Quinn (PQ) transformations.

Physical Review D, 2009

We examine few simple extremal black hole configurations of N = 8, d = 4 supergravity. We first elucidate the relation between the BPS Reissner-Nördstrom black hole and the non-BPS Kaluza-Klein dyonic black hole. Their classical entropy, given by the Bekenstein-Hawking formula, can be reproduced via the attractor mechanism by suitable choices of symplectic frame. Then, we display the embedding of the axion-dilaton black hole into N = 8 supergravity.

Journal of High Energy Physics, 2008

We study the attractor equations for a quantum corrected prepotential F = t 3 + iλ, with λ ∈ R,which is the only correction which preserves the axion shift symmetry and modifies the geometry.

The European Physical Journal Plus, 2011

Quantum entanglement lies at the heart of quantum information theory, with applications to quantum computing, teleportation, cryptography and communication. In the apparently separate world of quantum gravity, the Bekenstein-Hawking entropy of black holes has also occupied center stage.

Journal of Physics A: Mathematical and Theoretical, 2011

Starting from basic identities of the group E 8 , we perform progressive reductions, namely decompositions with respect to the maximal and symmetric embeddings of E 7 × SU (2) and then of E 6 × U (1). This procedure provides a systematic approach to the basic identities involving invariant primitive tensor structures of various irreprs. of finite-dimensional exceptional Lie groups. We derive novel identities for E 7 and E 6 , highlighting the E 8 origin of some well known ones. In order to elucidate the connections of this formalism to four-dimensional Maxwell-Einstein supergravity theories based on symmetric scalar manifolds (and related to irreducible Euclidean Jordan algebras, the unique exception being the triality-symmetric N = 2 stu model), we then derive a fundamental identity involving the unique rank-4 symmetric invariant tensor of the 0-brane charge symplectic irrepr. of U-duality groups, with potential applications in the quantization of the charge orbits of supergravity theories, as well as in the study of multi-center black hole solutions therein.

International Journal of Modern Physics A, 2016

Fortschritte der Physik, 2007

We show that requiring unbroken supersymmetry everywhere in black-hole-type solutions of N = 2, d = 4 supergravity coupled to vector supermultiplets ensures in most cases absence of naked singularities. We show that the requirement of global supersymmetry implies the absence of sources for NUT charge, angular momentum, scalar hair and negative energy, for which there is no microscopic interpretation in String Theory. These conditions exclude, for instance, singular solutions such as the Kerr-Newman with M = |q|, which fails to be everywhere supersymmetric. There are, nevertheless, everywhere supersymmetric solutions with global angular momentum and non-trivial scalar fields. We also present similar preliminary results in N = 1, d = 5 supergravity coupled to vector multiplets.

Physical Review D, 2001

We revisit the physics of five-dimensional black holes constructed from D5-and D1-branes and momentum modes in type IIB string theory compactified on K3. Since these black holes incorporate D5-branes wrapped on K3, an enhançon locus appears in the spacetime geometry. With a "small" number of D1-branes, the entropy of a black hole is maximised by including precisely half as many D5-branes as there are D1-branes in the black hole. Any attempts to introduce more D5-branes, and so reduce the entropy, are thwarted by the appearance of the enhançon locus above the horizon, which then prevents their approach. The enhançon mechanism thereby acts to uphold the Second Law of Thermodynamics. This result generalises: For each type of bound state object which can be made of both types of brane, we show that a new type of enhançon exists at successively smaller radii in the geometry, again acting to prevent any reduction of the entropy just when needed. We briefly explore the appearance of the enhançon locus in the black hole interior.

Physical Review D, 2005

We present an ansatz for black 2-branes in five dimensional N = 2 supergravity theory that carry magnetic charge with respect to general hypermultiplet scalars. We find explicit solutions in certain special cases and examine the constraints on the general case. These branes may be thought of as arising from M-branes by wrapping eleven dimensional supergravity over special Lagrangian calibrated cycles of a Calabi-Yau 3-fold.

Physical Review D, 2006

We present explicit U-duality invariants for the R, C, Q, O (real, complex, quaternionic and octonionic) magic supergravities in four and five dimensions using complex forms with a reality condition. From these invariants we derive an explicit entropy function and corresponding stabilization equations which we use to exhibit stationary multi-center 1/2 BPS solutions of these N = 2 d = 4 theories, starting with the octonionic one with E 7(−25) duality symmetry. We generalize to stationary 1/8 BPS multicenter solutions of N = 8, d = 4 supergravity, using the consistent truncation to the quaternionic magic N = 2 supergravity. We present a general solution of non-BPS attractor equations of the STU truncation of magic models. We finish with a discussion of the BPS-non-BPS relations and attractors in N = 2 versus N = 5, 6, 8.

Physical Review D, 1999

We computed the statistical entropy of nonextremal 4D and extremal 5D Calabi-Yau black holes and found exact agreement with the Bekenstein-Hawking entropy. The computation is based on the fact that the near-horizon geometry of equivalent representations contains as a factor the Bañados-Teitelboim-Zanelli black hole and on subsequent use of Strominger's proposal generalizing the statistical count of microstates of the BTZ black hole due to Carlip.

Physical Review D, 2007

Recently it has been observed that the group E 7 can be used to describe a special type of quantum entanglement of seven qubits partitioned into seven tripartite systems. Here we show that this curious type of entanglement is entirely encoded into the discrete geometry of the Fano plane. We explicitly work out the details concerning a qubit interpretation of the E 7 generators as representatives of tripartite protocols acting on the 56 dimensional representation space. Using these results we extend further the recently studied analogy between quantum information theory and supersymmetric black holes in four-dimensional string theory. We point out that there is a dual relationship between entangled subsystems containing three and four tripartite systems. This relationship is reflected in the structure of the expressions for the black hole entropy in the N = 4 and N = 2 truncations of the E 7(7) symmetric area form of N = 8 supergravity. We conjecture that a similar picture based on other qubit systems might hold for black hole solutions in magic supergravities.

Physical Review D, 2007

Following the recent trend we develop further the black hole analogy between quantum information theory and the theory of extremal stringy black hole solutions. We show that the three-qubit interpretation of supersymmetric black hole solutions in the STU model can be extended also to include non-supersymmetric ones. First we show that the black hole potential can be expressed as one half the norm of a suitably chosen three-qubit entangled state containing the quantized charges and the moduli. The extremization of the black hole potential in terms of this entangled state amounts to either supressing bit flip errors (BPS-case) or allowing very special types of flips transforming the states between different classes of non-BPS solutions. We are illustrating our results for the example of the D2 − D6 system. In this case the bit flip errors are corresponding to sign flip errors of the charges originating from the number of D2 branes. After moduli stabilization the states depending entirely on the charges are maximally entangled graph-states (of the triangle graph) well-known from quantum information theory. An N = 8 interpretation of the STU-model in terms of a mixed state with fermionic purifications is also given.

Physical Review D, 2011

We link the recently discovered black hole-qubit correspondence to the structure of extra dimensions. In particular we show that for toroidal compactifications of type IIB string theory simple qubit systems arise naturally from the geometrical data of the tori parametrized by the moduli. We also generalize the recently suggested idea of the attractor mechanism as a distillation procedure of GHZ-like entangled states on the event horizon, to moduli stabilization for flux attractors in F-theory compactifications on elliptically fibered Calabi-Yau four-folds. Finally using a simple example we show that the natural arena for qubits to show up is an embedded one within the realm of fermionic entanglement of quantum systems with indistinguishable constituents.

Physical Review D, 2011

Concurrence is an entanglement measure characterizing the mixed state bipartite correlations inside of a pure state of an n-qubit system. We show that after organizing the charges and the moduli in the STU model of N = 2, d = 4 supergravity to a three-qubit state, for static extremal spherically symmetric BPS black hole solutions the vanishing condition for all of the bipartite concurrences on the horizon is equivalent to the attractor equations. As a result of this the macroscopic black hole entropy given by the three-tangle can be reinterpreted as a linear entropy characterizing the pure state entanglement for an arbitrary bipartite split. Both for the BPS and non-BPS cases explicit expressions for the concurrences are obtained, with their vanishing on the horizon is demonstrated.

Journal of High Energy Physics, 2006

By making use of the entropy function formalism we study the generalized attractor equations in the four dimensional N = 2 supergravity in presence of higher order corrections. This result might be used to understand a possible ensemble one could associate to an extremal black hole.

Classical and Quantum Gravity, 1999

In the context of N = 8 supergravity we consider BPS black-holes that preserve 1/8 supersymmetry. It was shown in a previous paper that, modulo U -duality transformations of E 7(7) the most general solution of this type can be reduced to a black-hole of the STU model. In this paper we analize this solution in detail, considering in particular its embedding in one of the possible Special Kähler manifold compatible with the consistent truncations to N = 2 supergravity, this manifold being the moduli space of the T 6 /Z Z 3 orbifold, that is: SU (3, 3)/SU (3) × U (3). This construction requires a crucial use of the Solvable Lie Algebra formalism. Once the goup-theoretical analisys is done, starting from a static, spherically symmetric ansätz, we find an exact solution for all the scalars (both dilaton and axion-like) and for gauge fields, together with their already known chargedependent fixed values, which yield a U -duality invariant entropy. We give also a complete translation dictionary between the Solvable Lie Algebra and the Special Kähler formalisms in order to let comparison with other papers on similar issues being more immediate. Although the explicit solution is given in a simplified case where the equations turn out to be more manageable, it encodes all the features of the more general one, namely it has non-vanishing entropy and the scalar fields have a non-trivial radial dependence.

Journal of High Energy Physics, 2019

Non-extremal black holes are endowed with geometric invariants related to their horizon areas. We extend earlier work on hot attractor black holes to higher dimensions and add a scalar potential. In addition to the event and Cauchy horizons, when we complexify the radial coordinate, non-extremal black holes will generically have other horizons as well. We prove that the product of all of the horizon areas is independent of variations of the asymptotic moduli further generalizing the attractor mechanism for extremal black holes. In the presence of a scalar potential, as typically appears in gauged supergravity, we find that the product of horizon areas is not necessarily the geometric mean of the extremal area, however. We outline the derivation of horizon invariants for stationary backgrounds.

Journal of High Energy Physics, 2008

We investigate the attractor mechanism in gauged supergravity in the presence of higher derivatives terms. In particular, we discuss the attractor behaviour of static black hole horizons in anti-de Sitter spacetime by using the effective potential approach as well as Sen's entropy function formalism. We use the holographic techniques to interpret the moduli flow as an RG flow towards the IR attractor horizon. We find that the holographic c-function obeys the expected properties and point out some subtleties in understanding attractors in AdS.

Journal of High Energy Physics, 2006

We apply Sen's entropy formalism to the study of the near horizon geometry and the entropy of asymptotically AdS black holes in gauged supergravities. In particular, we consider non-supersymmetric electrically charged black holes with AdS 2 × S d−2 horizons in U(1) 4 and U(1) 3 gauged supergravities in d = 4 and d = 5 dimensions, respectively. We study several cases including static/rotating, BPS and non-BPS black holes in Einstein as well as in Gauss-Bonnet gravity. In all examples, the near horizon geometry and black hole entropy are derived by extremizing the entropy function and are given entirely in terms of the gauge coupling, the electric charges and the angular momentum of the black hole.

Physical Review D, 2010

In a recent paper it has been shown that for double extremal static spherical symmetric BPS black hole solutions in the STU model the well-known process of moduli stabilization at the horizon can be recast in a form of a distillation procedure of a three-qubit entangled state of GHZ-type. By studying the full flow in moduli space in this paper we investigate this distillation procedure in more detail. We introduce a three-qubit state with amplitudes depending on the conserved charges the warp factor, and the moduli. We show that for the recently discovered non-BPS solutions it is possible to see how the distillation procedure unfolds itself as we approach the horizon. For the non-BPS seed solutions at the asymptotically Minkowski region we are starting with a three-qubit state having seven nonequal nonvanishing amplitudes and finally at the horizon we get a GHZ state with merely four nonvanishing ones with equal magnitudes. The magnitude of the surviving nonvanishing amplitudes is proportional to the macroscopic black hole entropy. A systematic study of such attractor states shows that their properties reflect the structure of the fake superpotential. We also demonstrate that when starting with the very special values for the moduli corresponding to flat directions the uniform structure at the horizon deteriorates due to errors generalizing the usual bit flips acting on the qubits of the attractor states.

Physical Review D, 2010

In this paper we describe the structure of extremal stationary spherically symmetric black hole solutions in the ST U model of D = 4, N = 2 supergravity in terms of four-qubit systems. Our analysis extends the results of previous investigations based on three qubits. The basic idea facilitating this four-qubit interpretation is the fact that stationary solutions in D = 4 supergravity can be described by dimensional reduction along the time direction. In this D = 3 picture the global symmetry group SL(2, R) ×3 of the model is extended by the Ehlers SL(2, R) accounting for the fourth qubit. We introduce a four qubit state depending on the charges (electric, magnetic and NUT) the moduli and the warp factor. We relate the entanglement properties of this state to different classes of black hole solutions in the STU model. In the terminology of four qubit entanglement extremal black hole solutions correspond to nilpotent, and nonextremal ones to semisimple states. In arriving at this entanglement based scenario the role of the four algebraically independent four qubit SL(2, C) invariants is emphasized.

Physical Review D, 2011

We relate the U-duality invariants characterizing two-center extremal black hole solutions in the stu, st 2 and t 3 models of N = 2, d = 4 supergravity to the basic invariants used to characterize entanglement classes of four-qubit systems. For the elementary example of a D0D4-D2D6 composite in the t 3 model we illustrate how these entanglement invariants are related to some of the physical properties of the two-center solution. Next we show that it is possible to associate elliptic curves to charge configurations of two-center composites. The hyperdeterminant of the hypercube, a four-qubit polynomial invariant of order 24 with 2894276 terms, is featuring the j invariant of the elliptic curve. We present some evidence that this quantity and its straightforward generalization should play an important role in the physics of two-center solutions.

Journal of High Energy Physics, 2007

We generalize the covariant c-map found in hep-th/0701214 including perturbative quantum corrections. We also perform explicitly the superconformal quotient from the hyperkähler cone obtained by the quantum c-map to the quaternion-Kähler space, which is the moduli space of hypermultiplets. As a result, the perturbatively corrected metric on the moduli space is found in a simplified form comparing to the expression known in the literature.

Physical Review D, 2010

Motivated by the new higher D-supergravity solutions on intersecting attractors obtained by Ferrara et al. in [ Phys.Rev.D79:065031-2009], we focus in this paper on 8D maximal supergravity with moduli space SL(3,R) SO(3) × SL(2,R) SO(2) and study explicitly the attractor mechanism for various configurations of extremal black pbranes (anti-branes) with the typical near horizon geometries AdS p+2 × S m × T 6−p−m and p = 0, 1, 2, 3, 4; 2 ≤ m ≤ 6. Interpretations in terms of wrapped M2 and M5 branes of the 11D M-theory on 3-torus are also given.

International Journal of Modern Physics A, 2017

We study the effect of Freudenthal duality on supersymmetric extremal black hole attractors in [Formula: see text], [Formula: see text] ungauged supergravity. Freudenthal duality acts on the dyonic black hole charges as an anti-involution which keeps the black hole entropy and the critical points of the effective black hole potential invariant. We analyze its effect on the recently discovered distinct, mutually exclusive phases of axionic supersymmetric black holes, related to the existence of nontrivial involutory constant matrices. In particular, we consider a supersymmetric [Formula: see text] black hole and we explicitly Freudenthal-map it to a supersymmetric [Formula: see text] black hole. We thus show that the charge representation space of a supersymmetric [Formula: see text] black hole also contains mutually exclusive domains.

Universe, 2017

In a recent paper [Mod. Phys. Lett. A30 (2015) 1550104], the black-hole/qubit correspondence (BHQC) was exploited to define "black hole quantum circuits" allowing for a change of the supersymmetry-preserving features of electromagnetic charge configurations supporting the black hole solution. This resulted into switching from one U-duality orbit to another, or-equivalently-from an element of the corresponding Freudenthal Triple System with a definite rank, to another one. On the supergravity side of BHQC, such quantum gates are related to particular symplectic transformations acting on the black hole charges; namely, such transformations cannot belong to the U-duality group, otherwise switching among orbits would be impossible. In this paper, we consider a particular class of such symplectic transformations, namely the ones belonging to the so-called Peccei-Quinn symplectic group, introduced some time ago within the study of very special Kähler geometries of the vector multiplets' scalar manifolds in N = 2 supergravity in D = 4 spacetime dimensions. Contribution to the "Universe" special issue titled "Open Questions in Black Hole Physics"

Journal of High Energy Physics, 2021

We consider the static, spherically symmetric and asymptotically flat BPS extremal black holes in ungauged N = 2 D = 4 supergravity theories, in which the scalar manifold of the vector multiplets is homogeneous. By a result of Shmakova on the BPS attractor equations, the entropy of this kind of black holes can be expressed only in terms of their electric and magnetic charges, provided that the inverse of a certain quadratic map (uniquely determined by the prepotential of the theory) is given. This inverse was previously known just for the cases in which the scalar manifold of the theory is a homogeneous symmetric space. In this paper we use Vinberg’s theory of homogeneous cones to determine an explicit expression for such an inverse, under the assumption that the scalar manifold is homogeneous, but not necessarily symmetric. As immediate consequence, we get a formula for the entropy of BPS black holes that holds in any model of N = 2 supergravity with homogeneous scalar manifold.

Physical Review D, 2000

Supersymmetry of five dimensional string solutions is examined in the context of gauged D = 5, N = 2 supergravity coupled to abelian vector multiplets. We find magnetic black strings preserving one quarter of supersymmetry and approaching the half-supersymmetric product space AdS 3 × H 2 near the event horizon. The solutions thus exhibit the phenomenon of supersymmetry enhancement near the horizon, like in the cases of ungauged supergravity theories, where the near horizon limit is fully supersymmetric. Finally, product space compactifications are studied in detail, and it is shown that only for negative curvature (hyperbolic) internal spaces, some amount of supersymmetry can be preserved. Among other solutions, we find that the extremal rotating BTZ black hole tensored by H 2 preserves one quarter of supersymmetry.

Journal of High Energy Physics, 2021

We analyze the charge-to-mass structure of BPS states in general infinite-distance limits of $$ \mathcal{N} $$ N = 2 compactifications of Type IIB string theory on Calabi-Yau three-folds, and use the results to sharpen the formulation of the Swampland Conjectures in the presence of multiple gauge and scalar fields. We show that the BPS bound coincides with the black hole extremality bound in these infinite distance limits, and that the charge-to-mass vectors of the BPS states lie on degenerate ellipsoids with only two non-degenerate directions, regardless of the number of moduli or gauge fields. We provide the numerical value of the principal radii of the ellipsoid in terms of the classification of the singularity that is being approached. We use these findings to inform the Swampland Distance Conjecture, which states that a tower of states becomes exponentially light along geodesic trajectories towards infinite field distance. We place general bounds on the mass decay rate λ of thi...

Journal of High Energy Physics, 2006

We consider theories with gravity, gauge fields and scalars in four-dimensional asymptotically flat space-time. By studying the equations of motion directly we show that the attractor mechanism can work for non-supersymmetric extremal black holes. Two conditions are sufficient for this, they are conveniently stated in terms of an effective potential involving the scalars and the charges carried by the black hole. Our analysis applies to black holes in theories with N 1 supersymmetry, as well as non-supersymmetric black holes in theories with N = 2 supersymmetry. Similar results are also obtained for extremal black holes in asymptotically Anti-de Sitter space and in higher dimensions.

Physical review, 2005

We consider theories with gravity, gauge fields and scalars in four-dimensional asymptotically flat space-time. By studying the equations of motion directly we show that the attractor mechanism can work for non-supersymmetric extremal black holes. Two conditions are sufficient for this, they are conveniently stated in terms of an effective potential involving the scalars and the charges carried by the black hole. Our analysis applies to black holes in theories with N 1 supersymmetry, as well as non-supersymmetric black holes in theories with N = 2 supersymmetry. Similar results are also obtained for extremal black holes in asymptotically Anti-de Sitter space and in higher dimensions.

Journal of High Energy Physics, 2019

We study the behaviour of extremal and near-extremal black holes at low energies and low temperatures and find that it can be understood from the near-horizon AdS 2 region. Our analysis includes charged matter and also goes beyond the S-wave approximation. We find that the leading behaviour at low energies arises from a mode linked to time reparametrisations and from phase modes arising from gauge fields. At somewhat higher energies, additional modes arising from higher partial waves can also be cumulatively significant. These results can be applied quite generally to cases where an AdS 2 × S d near-horizon geometry arises, including black holes in asymptotically AdS and flat space-times.

Advances in Mathematical Physics, 2019

A Kaluza-Klein state configuration in black-hole qubit correspondence (BHQC) is considered in cyclic cycles of its Bekenstein-Hawking entropy. After a sequence of Peccei-Quinn transformations on the Kaluza-Klein state in cyclic cycles alternating between large and small extremal black hole (EBH) configurations, we obtain the corresponding amount of variation in the initial Bekenstein-Hawking entropy in cyclic cycles. We consider different cases where the EBH state alternates between small and large states. We then demonstrate that the total Bekenstein-Hawking entropy increases in these processes.