Notes on branes in matrix theory

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 non-compact 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