Non-Geometric Heterotic Vacua from Type II$_0$ Loci

Abstract

We determine 4d $\mathcal{N}=2$ heterotic string backgrounds dual to Type IIB string theory compactified on Calabi--Yau threefolds containing a type II$_0$ locus in their complex structure moduli space. While previous work only established the existence of such a duality frame, we concretely identify the heterotic theories dual to one- and two-parameter models exhibiting such loci, yielding novel instances of Type IIB--heterotic duality. To establish the correspondence, we first match the massless $\mathcal{N}=2$ spectrum, which uniquely fixes the heterotic data. We then recover the light spectrum of BPS D3-branes wrapping cycles on the Type IIB side from the heterotic perspective, and finally match the duality groups governing the global structure of the vector multiplet moduli space. All resulting heterotic theories are genuinely lower-dimensional, as they do not admit a decompactification limit to ten dimensions in their hypermultiplet moduli space. We identify two classes of duals. In the first, the heterotic string is compactified on a geometric K3 with a standard gauge bundle, demonstrating explicitly that type II$_0$ loci admit a consistent description as weakly coupled heterotic strings. In the second, the heterotic string background is given by a string-scale K3 and is hence non-geometric and genuinely four-dimensional. In this case, directly establishing supersymmetry would require control over all perturbative and non-perturbative $α'$ corrections. Here, the duality to Type IIB is most powerful, as it establishes the existence of new consistent, supersymmetric, and anomaly-free heterotic compactifications beyond the reach of conventional geometric methods. Finally, the Type IIB realization of the two-parameter models reveals that four-dimensional heterotic compactifications admit smooth transitions involving the nucleation of NS5-branes.