monopole, one can watch the formation of a string that connects the monopole to the two-brane. Test brane solutions were also studied in [@Im; @CGS] for the case of a fundamental string stretching between a D5-brane and a D3-brane, but in this case one must work much harder to solve the differential equations for the BPS configuration as one does not have the shortcut of simply looking for holomorphic curves.

Supergravity Solutions and a Puzzle {#puz}
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It is interesting, however, to go one step further and to solve for the full supergravity solutions beyond the test brane approximation; i.e., to go to the stage in which both branes are actively coupled to the bulk field. One would expect that this would show a ‘back-reaction’ of the D2-brane on the D6-brane. It turns out that such solutions can in fact be constructed in what is known as the ‘near-core limit’ using a simple trick introduced by [@ITY; @Aki].

The key point is that the charge N IIA D6-brane solution lifts to the charge N Kaluza-Klein monopole solution in M-theory. In particular, for the unit charge case the M-theory solution is completely smooth and so is well approximated by flat space 