On the Eleven-Dimensional Origins of Polarized D0-branes

TL;DR

This paper explores the eleven-dimensional origins of polarized D0-branes, deriving superpartners of the graviton, and analyzing their implications for supergravity solutions and Matrix theory, revealing new insights into their multipole moments and geometries.

Contribution

It introduces a novel eleven-dimensional perspective on polarized D0-branes by deriving superpartners of the graviton and analyzing their effects on supergravity solutions and Matrix theory.

Findings

Superpartners of the eleven-dimensional graviton are derived.

Polarized D0-brane solutions are obtained via dimensional reduction.

Dipole moments are formally infinite in non-asymptotically flat spacetime.

Abstract

The worldvolume theory of a D0-brane contains a multiplet of fermions which can couple to background spacetime fields. This coupling implies that a D0-brane may possess multipole moments with respect to the various type IIA supergravity fields. Different such polarization states of the D0-brane will thus generate different long-range supergravity fields, and the corresponding semi-classical supergravity solutions will have different geometries. In this paper, we reconsider such solutions from an eleven-dimensional perspective. We thus begin by deriving the ``superpartners'' of the eleven-dimensional graviton. These superpartners are obtained by acting on the purely bosonic solution with broken supersymmetries and, in theory, one can obtain the full BPS supermultiplet of states. When we dimensionally reduce a polarized supergraviton along its direction of motion, we recover a metric which describes a polarized D0-brane. On the other hand, if we compactify along the retarded null direction we obtain the short distance, or ``near-horizon'', geometry of a polarized D0-brane, which is related to finite $N$ Matrix theory. The various dipole moments in this case can only be defined once the eleven-dimensional metric is ``regularized'' and, even then, they are formally infinite. We argue, however, that this is to be expected in such a non-asymptotically flat spacetime. Moreover, we find that the superpartners of the D0-brane, in this $r \ra 0$ limit, possess neither spin nor D2-brane dipole moments.