Three-branes and five-branes in N=1 dual string pairs

Abstract In this note we show that in dual N =1 string vacua provided by the heterotic string on an elliptic Calabi-Yau together with a vector bundle respectively F -theory on Calabi-Yau fourfold the number of heterotic fivebranes necessary for anomaly cancellation matches the number of F -theory threebranes necessary for tadpole cancellation. This extends to the general case the work of Friedman, Morgan and Witten, who treated the case of embedding a heterotic E 8 × E 8 bundle, leaving no unbroken gauge group, where one has a smooth Weierstrass model on the F -theory side.