Octonions and Quantum Gravity through the Central Charge Anomaly in the Clifford Algebra
Abstract
We derive a theory of quantum gravity containing an AdS3 isometry/qubit duality. The theory is based on a superalgebra generalization of the enveloping algebra of the homogeneous AdS3 spacetime isometry group and is isomorphic to the complexified octonion algebra through canonical quantization. Its first three quaternion generators correspond to an -quantized AdS3 embedded spacetime and its remaining four non-quaternion generators to a G-quantized embedding 2+2 Minkowski spacetime. The quaternion algebra's expression after a monomorphism into the complexified Clifford algebra produces a two-dimensional conformal operator product expansion with a central charge anomaly, which results in an area-law G scaling satisfying the holographic principle and defines an "arrow of time". This relationship allows us to extend the theory through supersymmetry- and conformal-breaking O(G) transformations of the embedding to produce perturbed AdS3 spacetimes and derive a resolution to the black hole information paradox with an explicit mechanism.