Geometries, non-geometries, and fluxes

Abstract

Using F-theory/heterotic duality, we describe a framework for analyzing non-geometric $T_2$-fibered heterotic compactifications to six- and four dimensions. Our results suggest that among $T_2$-fibered heterotic string vacua, the non-geometric compactifications are just as typical as the geometric ones. We also construct four-dimensional solutions that have novel type-IIB and M-theory dual descriptions. These duals are non-geometric with three- and four-form fluxes not of (2, 1) or (2, 2) Hodge type, respectively, and yet preserve at least $N = 1$ supersymmetry.