YM on the dielectric brane: a D0-brane tale

TL;DR

This paper derives the Yang-Mills theory dynamics on a dielectric D2-brane from the D0-brane perspective, emphasizing the importance of residual non-commutativity in the large N limit for accurate mapping.

Contribution

It provides a derivation of the dielectric D2-brane's Yang-Mills dynamics from D0-branes, highlighting the necessity of residual non-commutativity in the large N limit.

Findings

Residual non-commutativity is essential for the Seiberg-Witten map.

Large N limit of fuzzy sphere relates to dielectric D2-brane.

Connection differs from the usual commutative D2-brane interpretation.

Abstract

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.