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

$D$-brane dynamics in constant Ramond-Ramond potentials, $S$-duality and noncommutative geometry