Oblate, Toroidal, and Other Shapes for the Enhancon

We present some results of studying certain axially symmetric supergravity geometries corresponding to a distribution of BPS D6-branes wrapped on K3, obtained as extremal limits of a rotating solution. The geometry's unphysical regions resulting from the wrapping can be repaired by the enhancon mechanism, with the result that there are two nested enhancon shells. For a range of parameters, the two shells merge into a single toroidal surface. Given the quite intricate nature of the geometry, it is an interesting system in which to test previous techniques that have been brought to bear in spherically symmetric situations. We are able to check the consistency of the construction using supergravity surgery techniques, and probe brane results. Implications for the Coulomb branch of (2+1)-dimensional pure SU(N) gauge theory are extracted from the geometry. Related results for wrapped D4- and D5-brane distributions are also discussed.