Compactifications of F-Theory on Calabi--Yau Threefolds -- II

TL;DR

This work extends F-theory compactifications on elliptic Calabi–Yau threefolds to a broader landscape, providing a concrete recipe to build F-theory duals for heterotic vacua in arbitrary dimensions and revealing a geometric fiber/base exchange that geometrizes string/string duality. It systematically analyzes 6D N=1 vacua, detailing how gauge groups and matter arise from Weierstrass data and Kodaira fibers across a wide range of instanton configurations, including cases with extra singularities and tensionless strings. The paper also studies the base geometry and showcases numerous examples (blown-up bases, Voisin–Borcea constructions, and orbifolds), then develops and analyzes extremal transitions among elliptically fibered CY3s, linking these to E8-instanton transitions and potential Argyres–Douglas-like points in 4D. Overall, it presents both a unifying geometric framework for N=1 d=6 vacua and a rich set of transitions and dualities that illuminate the role of (0,4) fivebranes and exceptional groups in F-theory/heterotic settings.

Abstract

We continue our study of compactifications of F-theory on Calabi--Yau threefolds. We gain more insight into F-theory duals of heterotic strings and provide a recipe for building F-theory duals for arbitrary heterotic compactifications on elliptically fibered manifolds. As a byproduct we find that string/string duality in six dimensions gets mapped to fiber/base exchange in F-theory. We also construct a number of new $N=1$, $d=6$ examples of F-theory vacua and study transitions among them. We find that some of these transition points correspond upon further compactification to 4 dimensions to transitions through analogues of Argyres--Douglas points of $N=2$ moduli. A key idea in these transitions is the notion of classifying $(0,4)$ fivebranes of heterotic strings.

Figures (4)

• Figure 1: The Voisin--Borcea examples.
• Figure 2: The extremal contraction with $n=4$.
• Figure 3: The F-theory moduli space on the boundary of the enlarged Kähler moduli space.
• Figure 4: The flop and extremal contraction with $n=1$.