Resolving brane collapse with 1/N corrections in non-Abelian DBI

A collapsing spherical D2-brane carrying magnetic flux can be described in the region of small radius in a dual zero-brane picture using Tseytlin's proposal for a non-Abelian Dirac-Born-Infeld action for N D0-branes. A standard large N approximation of the D0-brane action, familiar from the brane dielectric effect, gives a time evolution which agrees with the Abelian D2-brane Born-Infeld equations which describe a D2-brane collapsing to zero size. The first 1/N correction from the symmetrised trace prescription in the zero-brane action leads to a class of classical solutions where the minimum radius of a collapsing D2-brane is lifted away from zero. We discuss the validity of this approximation to the zero-brane action in the region of the minimum, and explore higher order 1/N corrections as well as an exact finite N example. The 1/N corrected Lagrangians and the finite N example have an effective mass squared which becomes negative in some regions of phase space. We discuss the physics of this tachyonic behaviour.