D-Brane Dynamics in Constant Ramond-Ramond Potentials, S-Duality and Noncommutative Geometry

TL;DR

This paper develops a formalism to analyze D-branes in constant Ramond-Ramond backgrounds, revealing a modified gauge field strength that respects S-duality and leads to noncommutative geometry, differing from traditional assumptions.

Contribution

It introduces a new formalism for open strings in gauge trivial closed string backgrounds and derives a novel expression for the gauge field strength on D-branes.

Findings

The gauge field strength is F=(1/2)(B-*C^(p-1)), not F=B.

The result is consistent with S-duality and leads to a S-dual invariant Moyal deformation.

The formalism applies to both RNS and Berkovits' covariant string theories.

Abstract

We study the physics of D-branes in the presence of constant Ramond-Ramond potentials. In the string field theory context, we first develop a general formalism to analyze open strings in gauge trivial closed string backgrounds, and then apply it both to the RNS string and within Berkovits' covariant formalism, where the results have the most natural interpretation. The most remarkable finding is that, in the presence of a Dp-brane, both a constant parallel NS-NS B-field and R-R C^(p-1)-field do not solve the open/closed equations of motion, and induce the same non-vanishing open string tadpole. After solving the open string equations in the presence of this tadpole, and after gauging away the closed string fields, one is left with a U(1) field strength on the brane given by F=(1/2)(B-*C^(p-1)), where * is Hodge duality along the brane world-volume. One observes that this result differs from the usually assumed result F=B. Technically, this is due to the fact that supersymmetric and bosonic string world-sheet theories are different. Note, however, that the usual F+B combination is still the combination which remains gauge invariant at the sigma-model level. Also, the standard result F=B is, in the D3-brane case, not compatible with S-duality. On the other hand our result, which is derived automatically given the general formalism, offers a non-trivial check of S-duality, to all orders in F, and this leads to a S-dual invariant Moyal deformation. In an appendix, we solve the source equation describing the open superstring in a generic NS-NS and R-R closed string background, within the super Poincare covariant formalism.