the circle will again give some smooth field, this conclusion also holds in cases where the 11-dimensional solution does not have an exact translation symmetry along $\lambda_{11}$ but which can be treated perturbatively. The same argument also applies to the dual field, so that $*\widetilde{F}_4=*_{11}F_{4}^{\{ 11 \} }$ should also vanish at a D6-brane. Here $*_{11}$ is the eleven-dimensional Hodge dual. This is the flux that causes D6-branes to produce fundamental strings, so no fundamental string charge should be induced on a D6-brane when a D2-brane is dragged past it. This is also related to a surprising property of a T-dual type IIB solution [@Tdual] involving D5-branes and Kaluza-Klein monopoles.

A similar sort of flux-excluding property was studied in [@sup]. For the ‘superconducting’ branes considered in that work, the normal component of some field strength was forced to vanish on the horizon. The situation here is somewhat different, however, as now the entire field strength $H_3$ or $*\widetilde{F}_4$ must vanish at the brane.

Although the above 11-dimensional argument for flux-expulsion meshes nicely with the unexpected results of [@GM] and [@Tdual], certain aspects of this story remain quite puzzling. For example, flux is clearly not expelled from the NS5-brane or from 