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Black holes, qubits and octonions

Although nominally a review of the ''black hole/qubit correspondence'' introduced by Duff in 2006 and covering work by Duff and collaborators 2006-2008, this paper also contains original results that have influenced thought in black hole physics, quantum information theory and mathematics. Specifically section 9 on Freudenthal triples has led to a new symmetry of supergravity known as Freudenthal duality, pursued by Zumino and others (arxiv:1208.0013, 1212.3254). In sections 8.3 to 8.6 on octonions and the Fano plane form the basis of a new approach to string/M-theory based on the four division algebras: real, complex, quaternion and octonions (RCHO) that goes beyond just their utility in black hole physics. For example, this has led to a formulation of N=1,2,4,8 Yang-Mills as a single theory over R, C, H, O. Regarding gravity as the product of two Yang-Mills theories then yields a ’’magic square’’ of supergravities (arxiv:1301.4176). These results go some way to fulfilling the promise of the role of octonions in M-theory discussed in section 15.2 but we believe this is just the tip of the iceberg. Other original sections are 13, which explores a more exotic version of the black-hole/qubit correspondence based on the octonionic quantum mechanics of Jordan,Von Neumann and Wigner, and Appendices C and D on the role of E8 in quantum information theory.