Geometries, Non-Geometries, and Fluxes

TL;DR

Geometries, Non-Geometries, and Fluxes investigates non-geometric heterotic compactifications using heterotic–F-theory duality, showing that non-geometric T^2-fibered vacua are as typical as geometric ones, with both $\tau$ and $\rho$ varying over a base and monodromies in $SL(2,\mathbb{Z})$. The authors develop a framework to extract classical data via duality even when no large-volume limit exists, and construct four-dimensional solutions with novel Type IIB and M-theory dual descriptions where fluxes need not be of $(2,1)$ or $(2,2)$ Hodge type yet preserve at least $\mathcal{N}=1$ supersymmetry. They analyze tadpoles and Bianchi identities in the presence of torsion and non-geometric patches, presenting explicit torsional heterotic backgrounds and their duals, including lifts to M-theory on $K3$-fibered Calabi–Yau four-folds that realize U-fold structures. The work broadens the landscape of viable vacua and clarifies how geometric and quantum heterotic data interrelate through dualities, with implications for flux compactifications and non-geometric string backgrounds.

Abstract

Using F-theory/heterotic duality, we describe a framework for analyzing non-geometric T2-fibered heterotic compactifications to six- and four-dimensions. Our results suggest that among T2-fibered heterotic string vacua, the non-geometric compactifications are just as typical as the geometric ones. We also construct four-dimensional solutions which 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.

Figures (5)

• Figure 1: A schematic of the desired fibration data where $u$ denotes coordinates on the base $B$. The loci of $\tau$ and $\rho$ degenerations can be viewed as supporting $5$-branes.
• Figure 2: Schematic of the duality chain that we use to generate non-geometric heterotic solutions with flux.
• Figure 3: The duality chain used to generate the heterotic solutions in the previous section as well as their type IIB and M-theory dual descriptions. The bold face indicates new solutions discussed in this paper.
• Figure 4: Fibration structure of the type IIB ${\cal M}_3$ solution.
• Figure 5: Fibration structure of the $\widetilde{{\cal M}}_4$ solution.