Multiple Dp-branes in weak background fields

We find the terms in the non-abelian world-volume action of a system of man y Dp-branes which describe the leading coupling to all type IT supergravity background fields. These results are found by T-dualizing earlier results for D0-branes, which in turn were determined from calculations of the M(atr ix) theory description of the supercurrent of 11D supergravity. Our results are compatible with earlier results on the supersymmetric Born-Infeld acti on for a single D-brane in a general background and with Tseytlin's symmetr ized trace proposal for extending the abelian Born-Infeld action to a non-a belian theory. In the case p = 3, the operators we find on the D-brane worl d-volume are closely related to those which couple to supergravity fields i n the AdS(5) x S-5 IIB supergravity background. This gives an explicit cons truction, including normalization, of some of the operators used in the cel ebrated AdS/CFT correspondence for 3-branes, We also discuss the S-duality of the action in the case p = 3, finding that the S-duality of the action d etermines how certain operators in the N = 4 4D SYM theory transform under S-duality, These S-duality results give some new insight into the puzzle of the transverse 5-brane in M(atrix) theory. (C) 2000 Elsevier Science B.V. All rights reserved.