Graph Theory and Qubit Information Systems of Extremal Black Branes
arXiv:1406.2578 · doi:10.1088/1751-8113/48/4/045401
Abstract
Using graph theory based on Adinkras, we consider once again the study of extremal black branes in the framework of quantum information. More precisely, we propose a one to one correspondence between qubit systems, Adinkras and certain extremal black branes obtained from type IIA superstring compactified on T^n. We accordingly interpret the real Hodge diagram of T^n as the geometry of a class of Adinkras formed by 2^n bosonic nodes representing n qubits. In this graphic representation, each node encodes information on the qubit quantum states and the charges of the extremal black branes built on T^n. The correspondence is generalized to n superqubits associated with odd and even geometries on the real supermanifold T^{n|n}. Using a combinatorial computation, general expressions describing the number of the bosonic and the fermionic states are obtained.
arXiv comment19 pages, Latex. References updated and minor changes added. A comment on Calabi-Yau manifolds is added. Final version accepted in J. Phys.A: Math.Theor.(2015)
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