Multiple D0-branes in weakly curved backgrounds

We investigate further our recent proposal for the form of the matrix theor y action in weak background fields, Using Seiberg's scaling argument we rel ate the matrix theory action to a low-energy system of many D0-branes in an arbitrary but weak NS-NS and R-R background. The resulting multiple D0-bra ne action agrees with the known Born-Infeld action in the case of a single brane and gives an explicit formulation of many additional terms which appe ar in the multiple brane action. The linear coupling to an arbitrary backgr ound metric satisfies the nontrivial consistency condition suggested by Dou glas that the masses of off-diagonal fields are given by the geodesic dista nce between the corresponding pair of D0-branes. This agreement arises from combinatorial factors which depend upon the symmetrized trace ordering pre scription found earlier for higher moments of the matrix theory stress-ener gy tensor. We study the effect of a weak background metric on two graviton interactions and find that our formalism agrees with the results expected f rom supergravity. The results presented here can be T-dualized to give expl icit formulae for the operators in any D-brane world-volume theory which co uple linearly to bulk gravitational fields and their derivatives. (C) 1999 Published by Elsevier Science B.V. All rights reserved.