Brane Mechanics

TL;DR

This paper explores two classes of one-dimensional brane solutions in supergravity backgrounds, analyzing their dynamics and phase structure through symmetry and orbit methods, revealing how brane interactions depend on energy and angular momentum.

Contribution

It introduces a unified approach to describe brane configurations using orbit parameters and analyzes their phase behavior in supergravity backgrounds.

Findings

Different phases of brane motion are characterized by energy and angular momentum.

The solutions are described by effective potentials derived from symmetry considerations.

The study provides a framework for understanding brane interactions in various configurations.

Abstract

In this paper, we investigate about two physically distinct classes of the `one-dimensional' worldvolume solutions describing the status of an arbitrary brane in the presence of another arbitrary (flat) brane which supplies the required supergravity background. One of these classes concerns with a relative (transverse) motion of two parallel flat branes, while the other class is related to a static configuration in which one of the branes is flat and the other is curved as a cylindrical hypersurface. Global symmetries of the worldvolume theory are used to show that both types of these solutions are described by some sort of `planar orbits' which are specified by their `energy' and `angular momentum' $(E,l)$ parameters. We find that various phases of the `motion' along these orbits, for different values of $(E,l)$, are easily deduced from the curve of an $E$-dependent function of the relative `distance' between the two branes, which is somehow related to their mutual `effective potential'.