Notes on the Construction of the D2-brane from Multiple D0-branes

We investigate the correspondence between the D2-brane, which is described by the abelian Born-Infeld action, and multiple D0-branes, which are done by the nonabelian Born-Infeld action. We construct effective actions for the fuzzy cylinder, sphere and plane formed via D0-branes and compare these actions with those for the cylindrical, spherical and planar D2-brane. We show that in the continuous limit, the effective actions for the fuzzy D0-branes precisely coincide with those for the single D2-brane if both the fuzziness of the D0-brane and the area occupied per a unit of magnetic flux on the D2-brane are equal to $(2\pi\ell_s)^2$.