Born-Infeld particles and Dirichlet p-branes

TL;DR

This work develops a gravity-free, Born-Infeld worldvolume theory for Dirichlet p-branes, revealing a rich set of static and non-static configurations including BIons and catenoids. By exploiting hidden Poincaré invariances, dualities, and calibration theory, the paper constructs and analyzes BPS, non-BPS, and multi-centered brane solutions, along with their energetics and force balance properties. It highlights deep connections to maximal hypersurfaces, special Lagrangian and Cayley calibrations, and demonstrates how brane throats can host monopoles, vortices, and tribulations akin to black brane physics in supergravity. The results illuminate the geometric and topological underpinnings of brane dynamics, with implications for brane intersections, flux tubes, and the nonperturbative structure of string theory in a non-gravitational limit.

Abstract

Born-Infeld theory admits finite energy point particle solutions with $δ$-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.