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Abstract

A noncommutative geometric configuration of D1-branes is obtained by numeric methods. This configuration is a static BPS solution to the non-Abelian Born-Infeld action, which is dual to an Abelian BPS D3-brane solution with magnetic charges. These monopoles correspond to emergent D1-branes that are attached to the D3-brane's surface and span a transverse direction. In the non-Abelian geometry, there is a topology change from a single noncommutative two-sphere of infinite radius at one end into two isolated two-spheres at infinity, with asymptotically vanishing radii. Recent method for constructing an Abelian surface from a non-Abelian geometry is used on the D1-brane configuration to compare it to the Abelian D3-brane configuration. The D3-brane and the D1-brane pictures are expected to converge for large N, yet surprisingly good agreement is found for N only reaching as high as 6.