Notes on Branes in Matrix Theory

TL;DR

Keski-Vakkuri and Kraus show that in the $N\to\infty$ limit of Matrix theory, coordinate matrices map to covariant derivatives on brane worldvolumes, yielding gauge theories with constant background fields that reproduce the large-field Born–Infeld action. They apply this to infinite and wrapped membranes (p=2) and longitudinal fivebranes (p=4), obtaining worldvolume YM actions and correct tensions, with $T_2=T_0/(2\pi)$ and $T=2T_4=2T_0/(2\pi)^2$, and relate the D0 density to $2\sigma_0=\frac{1}{8\pi^2}\mathrm{Tr}(f\wedge f)$. They demonstrate a one-loop D0–D6+D0 scattering giving $V(r)=4\cdot\frac{3}{16}\frac{1}{F_0 r}$, which matches the supergravity result, supporting the Matrix theory–supergravity correspondence in this regime. The framework points to a unified approach to D-brane dynamics in Matrix theory and invites investigation of finite-$N$ extensions for broader applicability.

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.