Ramond-Ramond Couplings of Noncommutative D-branes

TL;DR

This paper derives the leading couplings of noncommutative D-branes to RR potentials in a constant B-field, revealing topological zero momentum couplings and smeared finite momentum couplings, and explores their implications for field redefinitions and dielectric effects.

Contribution

It introduces a string amplitude motivated proposal for RR couplings of noncommutative D-branes, including the Seiberg-Witten map and derivative-driven dielectric effects.

Findings

Zero momentum couplings are topological and involve noncommutative Chern characters.

Finite momentum couplings are described by smeared operators along open Wilson lines.

Evidence for a new derivative-driven dielectric effect.

Abstract

We propose the leading couplings, in an alpha' expansion, of noncommutative D-branes to RR potentials in a constant NSNS B-field for an arbitrary choice of noncommutative parameter. The proposal is motivated by some string amplitude computations. The zero momentum couplings are topological in nature and involve Elliott's noncommutative Chern character. The finite momentum couplings are given by smearing the zero momentum operators along an open Wilson line. Comparisons between the RR couplings in different descriptions lead to a better understanding of the field redefinitions between gauge field variables (the Seiberg-Witten map) and help constrain alpha' corrections. In particular we recover the Seiberg-Witten map conjectured by one of the authors in hep-th/0011125. We also discuss the dynamics of the transverse scalar fields and find evidence for a new derivative-driven dielectric effect.