D-particle polarizations with multipole moments of higher-dimensional branes

TL;DR

This paper explores the polarization states of D0-branes in type IIA string theory, revealing their multipole moments, interactions, and the underlying cancellations that occur between different dipole-dipole interactions.

Contribution

It introduces the detailed polarization states of D0-branes with higher multipole moments and analyzes their supergravity fields and interaction cancellations.

Findings

D0-branes possess nonzero D2-brane and H-dipole moments.

Precise cancellations occur between spin-spin and magnetic dipole-dipole interactions.

The gyromagnetic ratio for spinning D0-branes is g=1, leading to specific interaction cancellations.

Abstract

We study the polarization states of the D0-brane in type IIA string theory. In addition to states with angular momentum and magnetic dipole moments, there are polarization states of a single D0-brane with nonzero D2-brane dipole and magnetic H-dipole moments, as well as quadrupole and higher moments of various charges. These fundamental moments of the D0-brane polarization states can be determined directly from the linearized couplings of background fields to the D0-brane world-volume fermions. These couplings determine the long range supergravity fields produced by a general polarization state, which typically have non-zero values for all the bosonic fields of type IIA supergravity. We demonstrate the precise cancellation between spin-spin and magnetic dipole-dipole interactions and an analogous cancellation between 3-form and H-field dipole-dipole interactions for a pair of D0-branes. The first of these cancellations follows from the fact that spinning D0-brane states have gyromagnetic ratio g = 1, and the second follows from the fact that the ratio between the 3-form and H-field dipole moments is also 1 in natural units. Both of these relationships can be seen immediately from the couplings in the D0-brane world-volume action.