Multiple Dp-branes in weak background fields Original Research Article

We find the terms in the non-abelian world-volume action of a system of many Dp-branes which describe the leading coupling to all type II 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(atrix) theory description of the supercurrent of 11D supergravity. Our results are compatible with earlier results on the supersymmetric Born–Infeld action for a single D-brane in a general background and with Tseytlinʹs symmetrized trace proposal for extending the abelian Born–Infeld action to a non-abelian theory. In the case p=3, the operators we find on the D-brane world-volume are closely related to those which couple to supergravity fields in the AdS5×S5 IIB supergravity background. This gives an explicit construction, including normalization, of some of the operators used in the celebrated 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 determines 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.