D-branes and the Non-commutative Structure of Quantum Spacetime

TL;DR

This paper explores how D-branes and string interactions imply a non-commutative, quantized structure of spacetime at very short distances, linking quantum gravity effects with D-particle dynamics and uncertainty principles.

Contribution

It introduces a worldsheet approach using logarithmic conformal field theory to connect D-brane dynamics with non-commutative spacetime geometry and quantum gravity.

Findings

Spacetime structure is captured by the Zamolodchikov metric on D-brane moduli space.

String genus expansion induces spacetime quantization and uncertainty relations.

Short-distance D-particle probes suggest decoherence effects related to quantum gravity.

Abstract

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.