Branonium

TL;DR

This paper analyzes the classical bound states of brane/antibrane systems by studying the motion of a probe antibrane in background fields, revealing exact elliptical orbits in special cases and discussing their decay via radiation.

Contribution

It provides a detailed classical analysis of brane/antibrane orbits, including exact solutions for certain cases and estimates of decay times due to radiation.

Findings

Elliptical orbits are exact solutions in specific Dp-brane cases.

Orbits decay over time through radiation of massless modes.

The classical system resembles a central force problem with non-closed orbits.

Abstract

We study the bound states of brane/antibrane systems by examining the motion of a probe antibrane moving in the background fields of N source branes. The classical system resembles the point-particle central force problem, and the orbits can be solved by quadrature. Generically the antibrane has orbits which are not closed on themselves. An important special case occurs for some Dp-branes moving in three transverse dimensions, in which case the orbits may be obtained in closed form, giving the standard conic sections but with a nonstandard time evolution along the orbit. Somewhat surprisingly, in this case the resulting elliptical orbits are exact solutions, and do not simply apply in the limit of asymptotically-large separation or non-relativistic velocities. The orbits eventually decay through the radiation of massless modes into the bulk and onto the branes, and we estimate this decay time. Applications of these orbits to cosmology are discussed in a companion paper.