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The Role of Supersymmetry in the Black Hole PDF
By:Duminda Dahanayake
Published on 2010 by

This thesis explores the numerous relationships between the entropy of black hole solutionsin supergravity and the entanglement of multipartite systems in quantum informationtheory: the so-called black hole/qubit correspondence. We examine how, through the correspondence, the dyonic charges in the entropy ofsupersymmetric black hole solutions are directly matched to the state vector coefficientsin the entanglement measures of their quantum information analogues. Moreover the Udualityinvariance of the black hole entropy translates to the stochastic local operationsand classical communication (SLOCC) invariance of the entanglement measures. Severalexamples are discussed, with the correspondence broadening when the supersymmetricclassification of black holes is shown to match the entanglement classification of thequbit/qutrit analogues. On the microscopic front, we study the interpretation of D-brane wrapping configurationsas real qubits/qutrits, including the matching of generating solutions on blackhole and qubit sides. Tentative generalisations to other dimensions and qubit systemsare considered. This is almost eclipsed by more recent developments linking the nilpotentU-duality orbit classi cation of black holes to the nilpotent classi cation of complexqubits. We provide preliminary results on the corresponding covariant classi cation. We explore the interesting parallel development of supersymmetric generalisations ofqubits and entanglement, complete with two- and three-superqubit entanglement measures. Lastly, we briefly mention the supergravity technology of cubic Jordan algebrasand Freudenthal triple systems (FTS), which are used to: 1) Relate FTS ranks to threequbitentanglement and compute SLOCC orbits. 2) Define new black hole dualitiesdistinct from U-duality and related by a 4D/5D lift. 3) Clarify the state of knowledgeof integral U-duality orbits in maximally extended supergravity in four, five, and sixdimensions.

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