Neumann boundary conditions from Born–Infeld dynamics Original Research Article

We would like to show that certain excitations of the F-string/D3-brane system can be shown to obey Neumann boundary conditions by considering the Born–Infeld dynamics of the F-string (viewed as a 3-brane cylindrically wrapped on an S2). In the paper by Callan and Maldacena it was shown that excitations which are normal to both the string and the 3-brane behave as if they had Dirichlet boundary conditions at the point of attachment. Here we show that 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 Polchinskiʹs open string Neumann boundary condition dynamically. In the low energy limit ω→0, i.e. for wavelengths much larger than the string scale only a small fraction ∼ω4 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.