The octonionic membrane

Duff, M. J.; Evans, J. M.; Khuri, Ramzi R.; Lu, J.X.; Minasian, Ruben

doi:10.1016/s0920-5632(98)00163-7

Cited by 6 publications

(3 citation statements)

References 28 publications

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“…The equation (8.17) for α i = 0 has been explored before in the context of resolved membranes, see e.g. [21,22,23,24]. A case α 0 = 0 has been considered in [8], corresponding to a rotating resolved M2-brane but dα was taken to be (2,0) and (0,2) instead of (1,1) and traceless that we have here.…”

Section: Resolved Membranesmentioning

confidence: 99%

“…In the context of M-theory, there are corrections to the flux field equation. In particular, one has [26,27] 22) and this new condition is required for the existence of non-singular solutions. To summarize, the conditions (8.18) and (8.20) are necessary and sufficient for the existence of a resolved (non-singular), rotating and wrapped membrane solution of eleven-dimensional supergravity with transverse space a compact, connected without boundary Calabi-Yau manifold.…”

Section: Resolved Membranesmentioning

confidence: 99%

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Systematics of M-theory spinorial geometry

Gran

Papadopoulos

Roest

2005

Class. Quantum Grav.

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We reduce the classification of all supersymmetric backgrounds in eleven dimensions to the evaluation of the supercovariant derivative and of an integrability condition, which contains the field equations, on six types of spinors. We determine the expression of the supercovariant derivative on all six types of spinors and give in each case the field equations that do not arise as the integrability conditions of Killing spinor equations. The Killing spinor equations of a background become a linear system for the fluxes, geometry and spacetime derivatives of the functions that determine the spinors. The solution of the linear system expresses the fluxes in terms of the geometry and specifies the restrictions on the geometry of spacetime for all supersymmetric backgrounds. We also show that the minimum number of field equations that is needed for a supersymmetric configuration to be a solution of eleven-dimensional supergravity can be found by solving a linear system. The linear systems of the Killing spinor equations and their integrability conditions are given in both a timelike and a null spinor basis. We illustrate the construction with examples.

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Section: Resolved Membranesmentioning

confidence: 99%

Section: Resolved Membranesmentioning

confidence: 99%

Systematics of M-theory spinorial geometry

Gran

Papadopoulos

Roest

2005

Class. Quantum Grav.

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“…The reader is referred to [163] for extensive details including historical notes. Some interesting physical applications may be found in [164,165,166,167,168,169,170,171,172,173]. We note that the octonions also make their appearance in a QI context in [174,175], but their work seems unrelated to ours.…”

Section: Octonions and The Fano Planementioning

confidence: 74%

Black holes, qubits and octonions

et al. 2009

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We review the recently established relationships between black hole entropy in string theory and the quantum entanglement of qubits and qutrits in quantum information theory. The first example is provided by the measure of the tripartite entanglement of three qubits (Alice, Bob and Charlie), known as the 3-tangle, and the entropy of the 8-charge ST U black hole of N = 2 supergravity, both of which are given by the [SL(2)] 3 invariant hyperdeterminant, a quantity first introduced by Cayley in 1845. Moreover the classification of three-qubit entanglements is related to the classification of N = 2 supersymmetric ST U black holes. There are further relationships between the attractor mechanism and local distillation protocols and between supersymmetry and the suppression of bit flip errors. At the microscopic level, the black holes are described by intersecting D3-branes whose wrapping around the six compact dimensions T 6 provides the string-theoretic interpretation of the charges and we associate the three-qubit basis vectors, |ABC (A, B, C = 0 or 1), with the corresponding 8 wrapping cycles. The black hole/qubit correspondence extends to the 56 charge N = 8 black holes and the tripartite entanglement of seven qubits where the measure is provided by Cartan's E 7 ⊃ [SL(2)] 7 invariant. The qubits are naturally described by the seven vertices ABCDEF G of the Fano plane, which provides the multiplication table of the seven imaginary octonions, reflecting the fact that E 7 has a natural structure of an O-graded algebra. This in turn provides a novel imaginary octonionic interpretation of the 56 = 7 × 8 charges of N = 8: the 24 = 3 × 8 NS-NS charges correspond to the three imaginary quaternions and the 32 = 4 × 8 R-R to the four complementary imaginary octonions. We contrast this approach with that based on Jordan algebras and the Freudenthal triple system. N = 8 black holes (or black strings) in five dimensions are also related to the bipartite entanglement of three qutrits (3-state systems), where the analogous measure is Cartan's E 6 ⊃ [SL(3)] 3 invariant. Similar analogies exist for magic N = 2 supergravity black holes in both four and five dimensions. Despite the ubiquity of octonions, our analogy between black holes and quantum information theory is based on conventional quantum mechanics but for completeness we also provide a more exotic one based on octonionic quantum mechanics. Finally, we note some intriguing, but still mysterious, assignments of entanglements to cosets, such as the 4-way entanglement of eight qubits to E 8 /[SL (2)] 8 .

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A Geometric Construction of Solutions to 11D Supergravity

Teng

Guo

Phong

2019

Commun. Math. Phys.

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Necessary and sufficient conditions are provided for a class of warped product manifolds with non-vanishing flux to be supersymmetric solutions of 11D supergravity. Many non-compact, but complete solutions can be obtained in this manner, including the multi-membrane solution initially found by Duff and Stelle. In a different direction, an explicit 5-parameter moduli space of solutions to 11D supergravity is also constructed which can be viewed as non-supersymmetric deformations of the Duff-Stelle solution.

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The octonionic membrane

Cited by 6 publications

References 28 publications

Systematics of M-theory spinorial geometry

Systematics of M-theory spinorial geometry

Black holes, qubits and octonions

A Geometric Construction of Solutions to 11D Supergravity

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