$(α')^4$ corrections to the N=2 supersymmetric Born-Infeld action
We consider the N=2 supersymmetric Born-Infeld action and compute one-loop divergences quantizing the theory in N=1 superspace. We find that in the presence of non constant curvature the theory is not renormalizable. The structure of the $(α')^4$ counterterm, proportional to derivatives of the curvature, is consistent with effective action calculations from superstring theory.