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

TL;DR

This paper explores how multiple D0-branes can form a D2-brane by comparing their effective actions, showing they match in the continuous limit when certain parameters are equal.

Contribution

It constructs effective actions for fuzzy D0-brane configurations and demonstrates their equivalence to D2-brane actions under specific conditions.

Findings

Effective actions for fuzzy D0-branes match D2-brane actions in the continuous limit.

Matching occurs when fuzziness and magnetic flux area per unit are equal to (2πℓ_s)^2.

Provides a detailed comparison between nonabelian D0-brane and abelian D2-brane descriptions.

Abstract

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 $(2\pi\ell_s)^2$.