Chains of N=2, D=4 heterotic/type II duals

TL;DR

This work identifies multiple N=2 heterotic string models whose Type II duals lie on Calabi–Yau threefolds that are $K3$ fibrations. By starting from symmetric orbifold constructions and performing cascaded Higgsing, the authors reveal five chains of heterotic models, each associated with a sequence of CYs whose weighted-projective descriptions exhibit regular patterns and correspond to specific $K3$ singularity chains. They map these chains to Type II geometries using 6D duality and monodromy arguments, uncovering a web-like connectivity among dual pairs and highlighting cases where CYs in existing lists lack known heterotic duals. The study suggests toric geometry as a powerful framework to understand singular transitions and to develop a more systematic approach to dual construction in 4D $N=2$ theories.

Abstract

We report on a search for $N=2$ heterotic strings that are dual candidates of type II compactifications on Calabi-Yau threefolds described as $K3$ fibrations. We find many new heterotic duals by using standard orbifold techniques. The associated type II compactifications fall into chains in which the proposed duals are heterotic compactifications related one another by a sequential Higgs mechanism. This breaking in the heterotic side typically involves the sequence $SU(4)\rightarrow SU(3)\rightarrow $ $SU(2)\rightarrow 0$, while in the type II side the weights of the complex hypersurfaces and the structure of the $K3$ quotient singularities also follow specific patterns.