# Heterotic/type II Duality and Non-Geometric Compactifications

## TL;DR

This paper explores new dualities between non-geometric Calabi-Yau compactifications in type II string theory and T-fold compactifications in heterotic string theory, revealing complex automorphisms and modular invariance mechanisms.

## Contribution

It introduces a novel class of dualities connecting non-geometric Calabi-Yau and heterotic T-fold compactifications, including automorphisms beyond prime order.

## Key findings

- Type II compactification reduces to an asymmetric Gepner model.
- Heterotic duals are asymmetric toroidal orbifolds.
- Modular invariance is restored by circle twists and NS5-brane charge phases.

## Abstract

We present a new class of dualities relating non-geometric Calabi-Yau compactifications of type II string theory to T-fold compactifications of the heterotic string, both preserving four-dimensional $\mathcal{N}=2$ supersymmetry. The non-geometric Calabi-Yau space is a $K3$ fibration over $T^2$ with non-geometric monodromies in the duality group $O(\Gamma_{4,20})$; this is dual to a heterotic reduction on a $T^4$ fibration over $T^2$ with the $O(\Gamma_{4,20})$ monodromies now viewed as heterotic T-dualities. At a point in moduli space which is a minimum of the scalar potential, the type II compactification becomes an asymmetric Gepner model and the monodromies become automorphisms involving mirror symmetries, while the heterotic dual is an asymmetric toroidal orbifold. We generalise previous constructions to ones in which the automorphisms are not of prime order. The type II construction is perturbatively consistent, but the naive heterotic dual is not modular invariant. Modular invariance on the heterotic side is achieved by including twists in the circles dual to the winding numbers round the $T^2$, and this in turn introduces non-perturbative phases depending on NS5-brane charge in the type II construction.