Three-Branes and Five-Branes in N=1 Dual String Pairs

TL;DR

This paper demonstrates the matching of fivebranes in heterotic string theory with threebranes in F-theory within N=1 dual vacua, extending previous work to more general cases involving elliptic Calabi-Yau manifolds.

Contribution

It establishes a correspondence between heterotic fivebranes and F-theory threebranes in dual N=1 string vacua beyond previously studied smooth models.

Findings

Number of heterotic fivebranes matches F-theory threebranes for anomaly and tadpole cancellation.

Extends previous smooth Weierstrass model results to more general elliptic Calabi-Yau cases.

Supports duality consistency in more complex N=1 string compactifications.

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