F-theory duals of singular heterotic K3 mode

Understand

We study F-theory duals of singular heterotic K3 models that correspond to abelian toroidal orbifolds $T^4/Z_N$.

• While our focus is on the standard embedding, we also comment on models with Wilson lines and more general gauge embeddings.
• In the process of constructing the duals, we work out a Weierstrass description of the heterotic toroidal orbifold models, which exhibit singularities of Kodaira type $I_0^*, IV^*, III^*$, and $II^*$.
• This construction unveils properties like the instanton number per fixed point and a correlation between the orbifold order and the multiplicities in the Dynkin diagram.