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

TL;DR

The paper investigates the rich polarization structure of a D0-brane in type IIA string theory, showing that worldvolume fermions couple to background fields to produce a spectrum of multipole moments beyond mass and RR charge. It develops a systematic framework to compute linear and higher-order couplings, derives the resulting long-range supergravity fields, and demonstrates exact cancellations of dipole-dipole forces between D0-branes due to g=1 and related moment ratios. By organizing the 256 polarization states into an $SO(16)$-structured Fock space and providing explicit $J^{ij}$ and $D^{ijk}$ actions, the authors classify states and connect them to corresponding supergravity solutions and their near-field multipoles. The work suggests a broad landscape of BPS D0 superpartners and has implications for bound-state dynamics and the microstructure of black hole solutions in string theory.

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.