Nonabelian D-branes and Noncommutative Geometry

TL;DR

This paper explores the nonabelian world-volume action of coincident D-branes, highlighting how matrix-valued scalar fields lead to noncommutative geometries, with applications including dielectric effects, intersecting branes, and giant gravitons.

Contribution

It provides a detailed analysis of how noncommutative geometries naturally emerge in the dynamics of multiple D-branes through the nonabelian action.

Findings

Demonstrates dielectric polarization of D-branes into noncommutative shapes.

Shows noncommutative geometries in intersecting brane configurations.

Connects giant graviton physics with noncommutative structures.

Abstract

We discuss the nonabelian world-volume action which governs the dynamics of N coincident Dp-branes. In this theory, the branes' transverse displacements are described by matrix-valued scalar fields, and so this is a natural physical framework for the appearance of noncommutative geometry. One example is the dielectric effect by which Dp-branes may be polarized into a noncommutative geometry by external fields. Another example is the appearance of noncommutative geometries in the description of intersecting D-branes of differing dimensions, such as D-strings ending on a D3- or D5-brane. We also describe the related physics of giant gravitons.