Octonions and Quantum Gravity through the Central Charge Anomaly in the Clifford Algebra

Abstract

We derive a theory of quantum gravity containing an AdS$_3$ isometry/qubit duality. The theory is based on a superalgebra generalization of the enveloping algebra of the homogeneous AdS$_3$ spacetime isometry group and is isomorphic to the complexified octonion algebra through canonical quantization. Its first three quaternion generators correspond to an $\hbar$-quantized AdS$_3$ 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 $\hbar G$ scaling satisfying the holographic principle and defines an "arrow of time". This relationship allows us to extend the theory through supersymmetry- and conformal-breaking $\mathcal O(G)$ transformations of the embedding to produce perturbed AdS$_3$ spacetimes and derive a resolution to the black hole information paradox with an explicit mechanism.