Multiple Dp-branes in Weak Background Fields

TL;DR

This work derives the leading linear couplings of a system of N Dp-branes to weak type II supergravity backgrounds by applying T-duality to known D0-brane (matrix theory) results. It presents both NS-NS and RR couplings, organizes them via world-volume currents and their moments, and demonstrates consistency with abelian κ-symmetric brane actions and with Tseytlin's symmetrized-trace proposal. The analysis extends to D9 and via T-duality to all lower branes, and it explores S-duality for D3-branes, offering insights into transverse 5-branes in matrix theory. Applications to AdS/CFT include explicit operator mappings for brane absorptions and a proposed correspondence between matrix theory currents and SYM operators, highlighting how supersymmetry constraints shape the structure of the nonabelian action and its background couplings.

Abstract

We find the terms in the nonabelian 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 Tseytlin's symmetrized trace proposal for extending the abelian Born-Infeld action to a nonabelian 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 AdS_5 * S^5 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 4D N = 4 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.