Abstract
Eight-dimensional nongeometric heterotic strings were constructed as duals of F-theory on Λ1,1 ⊕ E8 ⊕ E7 lattice polarized K3 surfaces by Malmendier and Morrison. We study the structure of the moduli space of this construction. There are special points in this space at which the ranks of the non-Abelian gauge groups on the 7-branes in F-theory are enhanced to 18. We demonstrate that the enhanced rank-18 non-Abelian gauge groups arise as a consequence of the coincident 7-branes, which deform stable degenerations on the F-theory side. This observation suggests that the non-geometric heterotic strings include nonperturbative effects of the coincident 7-branes on the F-theory side. The gauge groups that arise at these special points in the moduli space do not allow for perturbative descriptions on the heterotic side.We also construct a family of elliptically fibered Calabi-Yau 3-folds by fibering K3 surfaces with enhanced singularities over ℙ1. Highly enhanced gauge groups arise in F-theory compactifications on the resulting Calabi-Yau 3-folds.
Highlights
We construct a family of elliptically fibered Calabi-Yau 3-folds by fibering K3 surfaces with enhanced singularities over P1
We investigate the structure of the moduli space parameterizing F-theory on elliptic K3 surfaces with E8E7 singularity with a section
We find that eightdimensional non-geometric heterotic strings at these points in the moduli are obtained as the transitions from geometric heterotic strings when 7-branes are coincident on the F-theory side
Summary
We briefly review F-theory compactification and the non-Abelian gauge groups that arise on 7-banes. When an elliptic fibration admits a global section, it admits a transformation to the Weierstrass form In this case, the type of a singular fiber can be determined from the vanishing orders of the Weierstrass coefficients. The property H ⊂ N S(S) that the Neron-Severi lattice N S(S) of a K3 surface S contains the hyperbolic plane H is equivalent [118] to the statement that the K3 surface S admits an elliptic fibration with a section. When a genus-one fibered K3 surface has a section, inside the Neron-Severi lattice N S(S), the orthogonal complement of the hyperbolic plane generated by the fiber and a section contains the information on the types of the singular fibers. (except for P1’s that intersect with the zero-section) P1 components of a singular fiber belong to the orthogonal complement of the hyperbolic plane inside the K3 lattice ΛK3. Λ2,18 is an even integral unimodular lattice of signature (2,18), and this is unique up to isometry
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
