YM on the dielectric brane: a D0-brane tale

In this letter we present a derivation, from the D0-brane picture, of the background monopole field and in general of the full dynamics of the Yang-Mills theory on the dielectric D2-brane of Myers. To do this we study the large N limit of the fuzzy sphere relevant to the dielectric solution. In contrast to the usual interpretation, where the commutative D2-brane picture arises directly from the large N limit of the D0-brane picture, we find that a residual non-commutativity must be preserved, in order to make the connection by means of the Seiberg-Witten map.