Neumann Boundary Conditions from Born-Infeld Dynamics

TL;DR

This paper demonstrates how certain excitations in the F-string/D3-brane system obey Neumann boundary conditions through Born-Infeld dynamics, showing that string endpoints can move freely on the brane and produce electromagnetic radiation.

Contribution

It provides a dynamic realization of Polchinski's Neumann boundary conditions in the F-string/D3-brane system using Born-Infeld theory.

Findings

String excitations are almost fully reflected with free endpoint movement.

In the low energy limit, minimal energy escapes as dipole radiation.

String endpoints behave like electric charges producing electromagnetic waves.

Abstract

We show that certain excitations of the F-string/D3-brane system can be shown to obey Neumann boundary conditions by considering Born-Infeld dynamics of the F-string (viewed as a 3-brane cylindrically wrapped on an $S_2$). Excitations which are coming down the string with a polarization along a direction parallel to the brane are almost completely reflected just as in the case of all-normal excitations, but the end of the string moves freely on the 3-brane, thus realizing Polchinski's open string Neumann boundary condition dynamically. In the low energy limit w -> 0, i.e. for wavelengths much larger than the string scale only a small fraction ~w^4 of the energy escapes in the form of dipole radiation. The physical interpretation is that a string attached to the 3-brane manifests itself as an electric charge, and waves on the string cause the end point of the string to freely oscillate and therefore produce electromagnetic dipole radiation in the asymptotic outer region.