  We study derivative corrections to the effective action for a single D-brane
in type II superstring theory coupled to constant background fields. In
particular, within this setting we determine the complete expression for the
(disk level) four-derivative corrections to the Born-Infeld part of the action.
We also determine 2n-form 2n-derivative corrections to the Wess-Zumino term.
Both types of corrections involve all orders of the gauge field strength, F.
The results are obtained via string sigma-model loop calculations using the
boundary state operator language. The corrections can be succinctly written in
terms of the Riemann tensor for a non-symmetric metric.
