Born-Infeld particles and Dirichlet p-branes

TL;DR

This paper explores solutions in Born-Infeld theory related to D-branes, including BIons, catenoidal configurations, and monopoles, revealing their geometric and topological properties and connections to supergravity and supersymmetry.

Contribution

It introduces new classical solutions in Born-Infeld theory, connecting brane configurations, monopoles, and special Lagrangian submanifolds, expanding understanding of D-brane dynamics.

Findings

BIons as point particle solutions with delta-function sources

Topologically non-trivial catenoidal solutions linking p-branes

Duality rotations yield monopole solutions satisfying Bogomol'nyi equations

Abstract

Born-Infeld theory admits finite energy point particle solutions with $\delta$-function sources, BIons. I discuss their role in the theory of Dirichlet $p$-branes as the ends of strings intersecting the brane when the effects of gravity are ignored. There are also topologically non-trivial electrically neutral catenoidal solutions looking like two $p$-branes joined by a throat. The general solution is a non-singular deformation of the catenoid if the charge is not too large and a singular deformation of the BIon solution for charges above that limit. The intermediate solution is BPS and Coulomb-like. Performing a duality rotation we obtain monopole solutions, the BPS limit being a solution of the abelian Bogolmol'nyi equations. The situation closely resembles that of sub and super extreme black-brane solutions of the supergravity theories. I also show that certain special Lagrangian submanifolds of ${\Bbb C}^p$, $p=3,4,5$, may be regarded as supersymmetric configurations consisting of $p$-branes at angles joined by throats which are the sources of global monopoles. Vortex solutions are also exhibited.