Exploring Novel Geometry in Heterotic/F-theory Dual Pairs

In this work we explore a set of dual heterotic/F-theory geometries corresponding to 4-dimensional, Ar = 1 supersymmetric compactifications. We present a class of simple Calabi-Yau 4-folds that provide well-defined backgrounds for F-theory, but for which the naive duality map to the heterotic vector bundle geometry appears to fail. In particular, we show that a class of 4-folds with generic E-7 symmetries lead in the dual heterotic theory to a class of SU(2) bundles which appear to violate quantization conditions arising from the spectral cover construction. We propose a resolution to this puzzle and verify it in several examples.