Nongeometric heterotic strings and dual F-theory with enhanced gauge groups

TL;DR

This paper explores the moduli space of eight-dimensional nongeometric heterotic strings dual to F-theory, revealing how special points with enhanced gauge groups relate to coincident 7-branes and nonperturbative effects.

Contribution

It demonstrates the origin of rank-18 gauge groups from coincident 7-branes and constructs Calabi-Yau 3-folds with highly enhanced gauge symmetries in F-theory.

Findings

Enhanced gauge groups arise at special moduli points.

Coincident 7-branes deform stable degenerations.

Nonperturbative effects are present in nongeometric heterotic strings.

Abstract

Eight-dimensional nongeometric heterotic strings were constructed as duals of F-theory on $\Lambda^{1,1}\oplus E_8\oplus E_7$ 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 $\mathbb{P}^1$. Highly enhanced gauge groups arise in F-theory compactifications on the resulting Calabi-Yau 3-folds.