Spacetime quantization from non-Abelian D-particle dynamics

We describe the short-distance properties of the spacetime of a system of D particles by viewing their matrix-valued coordinates as coupling constants of a deformed world-sheet σ model. We show that the Zamolodchikov metric on the associated moduli space naturally encodes properties of the non-Abelian dynamics, and from this we derive new spacetime uncertainty relations directly from the quantum string theory. The non-Abelian uncertainties exhibit decoherence effects which suggest the interplay of quantum gravity in multiple D-particle dynamics.