D-Brane Chemistry

TL;DR

This paper explores the dynamics and bound states of D-branes and orientifolds, revealing integrable relativistic motions, classical analogs to nonrelativistic systems, and connections to M-theory, with implications for brane interactions.

Contribution

It provides a detailed analysis of D-brane bound states, their relativistic and quantum behaviors, and links to M-theory, offering new insights into brane dynamics and stability.

Findings

Relativistic motion of probe D-branes is integrable by quadratures.

Special cases yield Keplerian conic sections and nonrelativistic analogs.

D-brane interactions at short distances avoid tachyon instability.

Abstract

We study several different kinds of bound states built from D-branes and orientifolds. These states are to atoms what branonium - the bound state of a brane and its anti-brane - is to positronium, inasmuch as they typically involve a light brane bound to a much heavier object with conserved charges which forbid the system's decay. We find the fully relativistic motion of a probe Dp'-brane in the presence of source Dp-branes is integrable by quadratures. Keplerian conic sections are obtained for special choices for p and p' and the systems are shown to be equivalent to nonrelativistic systems. Their quantum behaviour is also equivalent to the corresponding non-relativistic limit. In particular the p=6, p'=0 case is equivalent to a non-relativistic dyon in a magnetic monopole background, with the trajectories in the surface of a cone. We also show that the motion of the probe branes about D6-branes in IIA theory is equivalent to the motion of the corresponding probes in the uplift to M-theory in 11 dimensions, for which there are no D6-branes but their fields are replaced by a particular Taub-NUT geometry. We further discuss the interactions of D-branes and orientifold planes having the same dimension. this system behaves at large distances as a brane-brane system but at shorter distances it does not have the tachyon instability.