Higher derivative D-brane couplings from T-duality and scattering amplitudes

The Wess-Zumino coupling on D-branes in string theory is known to receive higher derivative corrections which couple the Ramond-Ramond potential to terms involving the square of the space-time curvature tensor. Consistency with T-duality implies that the brane action should also contain four-derivative couplings that involve the NS-NS B-field. T-duality is used to predict some of these couplings. Then I will describe string world-sheet computations which confirm the predicted couplings.