Spacetime Quantization from Non-abelian D-particle Dynamics

TL;DR

This paper explores how the non-abelian dynamics of D-particles lead to spacetime quantization and uncertainty relations, revealing quantum gravity effects through string theory and matrix models.

Contribution

It introduces a novel approach linking D-particle matrix coordinates with worldsheet deformations to derive spacetime uncertainty relations from string theory.

Findings

Derivation of new spacetime uncertainty relations

Identification of decoherence effects in D-particle dynamics

Connection between non-abelian interactions and spacetime quantization

Abstract

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 worldsheet $\sigma$-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.