  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
$E_8\times E_8$ bundle, leaving no unbroken gauge group, where one has a smooth
Weierstrass model on the F-theory side.

High Energy Physics - Theory