Heterotic/type II duality and non-geometric compactifications

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 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(Γ 4,20 ); this is dual to a heterotic reduction on a T 4 fibration over T 2 with the O(Γ 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.

Moduli spaces of non-geometric type II/heterotic dual pairs

“…On the heterotic side, they could be tought at first glance as T-folds consisting in T 4 fibrations over a T 2 with O(4, 20) monodromy twists. However, as was shown in [11], perturbative consistency of the heterotic model provides a different picture: the T 4 fiber has monodromies both around the cycles of the T 2 and around the cycles of the T-dual T 2 . The main goal of the present work is to analyze the moduli spaces of such dual pairs.…”

“…In this section we briefly summarize the construction of non-geometric Calabi-Yau backgrounds in type IIA string theories [12][13][14], as well as of their heterotic duals [11].…”

“…The heterotic duals of these compactifications were constructed in [11]. In the heterotic frame the moduli space M σ of eq.…”

“…Recently, we have discovered with Chris Hull a new type of N = 2 heterotic/type II dual pairs in four dimensions [11], based on previous works [12][13][14]. On the type IIA side, they can be understood as mirror-folds [15], more precisely as K3 fibrations over a JHEP09(2020)082 two-torus with transition functions involving mirrored automorphisms [14], that are stringy symmetries combining automorphisms of a K3 surface and of its mirror.…”

“…This work is organized as follows. In section 2 we review the construction of the nongeometric models of [11] from both type IIA and heterotic viewpoints. In section 3 we discuss the general structure of the vector multiplet moduli space as well as the duality groups appearing in the perturbative limits; an explicit computation of the one-loop corrections to the prepotential for some of the models is presented in subsection 3.5.…”