Non-Supersymmetric String-String Dualities via Enriques Surfaces

We propose non-supersymmetric analogues of 6d N=2 Type II/heterotic dualities via a quotient of a K3 surface: an Enriques surface. We start from Type~II strings on a K3 surface and construct orbifold theories using an involution of K3. We extract the massless and tachyonic spectra and identify the moduli spaces locally. We further reinterpret the constructions as Type 0A/0B strings compactified on an Enriques surface, and argue that the theories are dual to recently constructed non-supersymmetric heterotic asymmetric orbifolds.

💡 Research Summary

The paper constructs non‑supersymmetric analogues of the well‑known six‑dimensional N=2 Type II/heterotic dualities by exploiting the Enriques surface, which is obtained as a fixed‑point‑free Z₂ quotient of a K3 surface. Starting from the conventional supersymmetric duality—Type II strings compactified on K3 being dual to heterotic strings on T⁴ (or T⁵ for the IIB case)—the authors identify a common discrete symmetry h. On the heterotic side h acts as a lattice automorphism of the even self‑dual lattice Γ₃,₁₉, while on the Type II side it is realized geometrically as a free involution of the K3 surface. By quotienting both theories by h they obtain new backgrounds: Type II strings on an Enriques surface and heterotic strings on the corresponding asymmetric orbifold T⁴/Z₂ (or T⁵/Z₂).

The construction proceeds in several steps. First, the paper reviews the supersymmetric heterotic compactifications, detailing the lattice decomposition Γ_{d,d+16}=I_{d−2,d+6}⊕N_{2,10} and the resulting moduli space factorisation into Coulomb and Higgs branches. Next, the standard Type II compactification on K3 is recapitulated, including the untwisted and twisted sectors of the T⁴/Z₂ orbifold limit, the resulting N=(1,1) (IIA) and N=(2,0) (IIB) six‑dimensional supergravity multiplets, and the moduli spaces O(4,20)/