  A worldsheet approach to the study of non-abelian D-particle dynamics is
presented based on viewing matrix-valued D-brane coordinate fields as coupling
constants of a deformed sigma-model which defines a logarithmic conformal field
theory. The short-distance structure of spacetime is shown to be naturally
captured by the Zamolodchikov metric on the corresponding moduli space which
encodes the geometry of the string interactions between D-particles. Spacetime
quantization is induced directly by the string genus expansion and leads to new
forms of uncertainty relations which imply that general relativity at very
short-distance scales is intrinsically described by a non-commutative geometry.
The indeterminancies exhibit decoherence effects suggesting the natural
incorporation of quantum gravity by short-distance D-particle probes. Some
potential experimental tests are briefly described.
