Corrections to macroscopic supersymmetric black-hole entropy

We determine the corrections to the entropy of extremal black holes arising from terms quadratic in the Riemann tensor in N= 2, D = 4 supergravity the ories. We follow Wald's proposal to modify the Bekenstein-Hawking area law. The new entropy formula, whose value only depends on the electric/magnetic charges, is expressed in terms of a single holomorphic function and is con sistent with electric-magnetic duality. For string effective field theories arising from Calabi-Yau compactifications, our result for the entropy of a certain class of extremal black-hole solutions fully agrees with the count ing of microstates performed some time ago by Maldacena, Strominger, Witten and by Vafa. (C) 1999 Elsevier Science B.V. All rights reserved.