Non-abelian action of D0-branes from Matrix theory in the longitudinal 5-brane background

We study one-loop effective action of Berkooz-Douglas Matrix theory and obtain nonabelian action of D0-branes in the background field produced by longitudinal 5-branes. Since these 5-branes do not have D0-brane charge and are not present in BFSS Matrix theory, our analysis provides an independent test for the coupling of D-branes to general weak backgrounds proposed by Taylor and Van Raamsdonk from the analysis of the BFSS model. The proposed couplings appear in the Berkooz-Douglas effective action precisely as expected, which suggests the consistency of the two matrix models. We also point out the existence of the terms which are not given by the symmetrized trace prescription in the Matrix theory effective action. E-mail address: [email protected] † E-mail address: [email protected]