Notes on Branes in Matrix Theory

TL;DR

This paper derives effective field theories for various brane configurations in Matrix theory, showing their relation to known actions like Born-Infeld and matching supergravity results for brane interactions.

Contribution

It provides a systematic derivation of brane effective actions from Matrix theory, including noncompact branes and specific scattering processes, connecting to supergravity predictions.

Findings

Effective actions are Yang-Mills type with magnetic backgrounds.

D2-brane action matches the large magnetic field limit of Born-Infeld.

Potential between D6+D0 and D0-brane agrees with supergravity.

Abstract

We study the effective actions of various brane configurations in Matrix theory. Starting from the 0+1 dimensional quantum mechanics, we replace coordinate matrices by covariant derivatives in the large N limit, thereby obtaining effective field theories on the brane world volumes. Even for noncompact branes, these effective theories are of Yang-Mills type, with constant background magnetic fields. In the case of a D2-brane, we show explicitly how the effective action equals the large magnetic field limit of the Born-Infeld action, and thus derive from Matrix theory the action used by Polchinski and Pouliot to compute M-momentum transfer between membranes. We also consider the effect of compactifying transverse directions. Finally, we analyze a scattering process involving a recently proposed background representing a classically stable D6+D0 brane configuration. We compute the potential between this configuration and a D0-brane, and show that the result agrees with supergravity.