<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>8</mml:mn></mml:math>attractors

Ferrara, S.; Каллош, Рената

doi:10.1103/physrevd.73.125005

Cited by 101 publications

(105 citation statements)

References 45 publications

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“…For the non-BPS attractors of magic supergravities we have made used of this truncation to the STU model. Using the solutions of the non-BPS attractors for N 8 super-gravity presented in [9] we have found the general solutions of the non-BPS attractors for the N 2 STU model.…”

Section: Discussionmentioning

confidence: 99%

“…Since now we understand certain features on N 8 BPS and non-BPS black holes and their relation to N 2 BPS and non-BPS ones, as shown in Ref. [9], we may extend this relations also to include N 6 and N 5 theories.…”

Section: B N 2 Versus N 5 6 8 and Bps Versus Non-bpsmentioning

confidence: 99%

“…The ADM mass is defined via the asymptotic behavior of the timetime component of the metric, as In [9] simple algebraic attractor equations were derived for regular black holes of N 8 supergravity. These equations have 2 solutions: one BPS with 1=8 of unbroken supersymmetry and one non-BPS solution with all supersymmetries broken.…”

Section: Multicenter Casementioning

confidence: 99%

“…[5][6][7][8] was established for N > 2 by a generalization of the special geometry symplectic structure to all extended supergravities [9]. In particular, for N 8 supergravity a simple set of algebraic equations was established which describe regular BPS and non-BPS extremal black hole solutions.…”

Section: Introductionmentioning

confidence: 99%

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Magic supergravities,N=8and black hole composites

2006

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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 multicenter 1=2 Bogomol'nyi-Prasad-Sommerfield (BPS) solutions of these N 2 d 4 theories, starting with the octonionic one with E 7 ÿ25 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 BPSnon-BPS relations and attractors in N 2 versus N 5, 6, 8.

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Section: Discussionmentioning

confidence: 99%

Section: B N 2 Versus N 5 6 8 and Bps Versus Non-bpsmentioning

confidence: 99%

Section: Multicenter Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Magic supergravities,N=8and black hole composites

2006

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“…The large black hole solutions can be found [25] by solving the N 8 classical attractor equations [26] when at the attractor value the Z AB matrix, in normal form, becomes If the phase in (4.6) vanishes (which is the case if the configuration preserves at least 1=4 supersymmetry [17] For N 8, as for N 2, the large black holes correspond to the two classes of GHZ-type (entangled) states and small black holes to the separable or W class.…”

Section: The Black Hole Analogymentioning

confidence: 99%

E7and the tripartite entanglement of seven qubits

2007

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In quantum information theory, it is well known that the tripartite entanglement of three qubits is described by the group SL 2; C 3 and that the entanglement measure is given by Cayley's hyperdeterminant. This has provided an analogy with certain N 2 supersymmetric black holes in string theory, whose entropy is also given by the hyperdeterminant. In this paper, we extend the analogy to N 8. We propose that a particular tripartite entanglement of seven qubits, encoded in the Fano plane, is described by the exceptional group E 7 C and that the entanglement measure is given by Cartan's quartic E 7 invariant. For our purposes, the important properties of the hyperdeterminant are that it is a quartic invariant under SL 2 3 and under a triality that interchanges A, B, and D. These properties are valid whether the a ABD are complex, real, or integer.The hyperdeterminant makes its appearance in quantum information theory [2]. Let the three-qubit system ABD (Alice, Bob, and Daisy) be in a pure state j i, and let the components of j i in the standard basis be a ABD :(1.3)Then the three-way entanglement of the three qubits A, B, and D is given by the 3-tangle [3] 3 ABD 4jDeta ABD j:However, one of us recently found another physical application of this hyperdeterminant [4] by associating the eight components of a ABD with the four electric and four magnetic charges of the STU black hole in fourdimensional string theory [5] and showing that its entropy [6] is given byAs far as we can tell [4], the appearance of the Cayley hyperdeterminant in these two different contexts of stringy black hole entropy (where the a ABD are integers and the symmetry is SL 2; Z 3 ) and three-qubit quantum entanglement (where the a ABD are complex numbers and the symmetry is SL 2; C 3 ) is a purely mathematical coincidence. Nevertheless, it has already provided fascinating new insights [7,8] into the connections between strings, black holes, and quantum information. 1 The black holes described by Cayley's hyperdeterminant are those of N 2 supergravity coupled to three vector multiplets, where the symmetry is SL 2; Z 3 . One might therefore ask whether the black hole/information theory correspondence could be generalized. There are three generalizations we might consider:(1) N 2 supergravity coupled to l vector multiplets where the symmetry is SL 2; Z SO l ÿ 1; 2; Z and the black holes carry charges belonging to the 2; l 1 representation (l 1 electric plus l 1 magnetic).(2) N 4 supergravity coupled to m vector multiplets where the symmetry is SL 2; Z SO 6; 6 m; Z where the black holes carry charges belonging to the 2; 12 m representation (m 12 electric plus m 12 magnetic). * m.duff@imperial.ac.uk † Sergio.Ferrara@cern.ch 1 A third application [9], not considered in this paper, is the Nambu-Goto string whose action is also given by jDeta ABD j p in spacetime signature (2, 2).

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