Abstract
We consider compactifications of type IIA superstring theory on mirror-folds obtained as K3 fibrations over two-tori with non-geometric monodromies involving mirror symmetries. At special points in the moduli space these are asymmetric Gepner models. The compactifications are constructed from non-geometric automorphisms that arise from the diagonal action of an automorphism of the K3 surface and of an automorphism of the mirror surface. We identify the corresponding gaugings of mathcal{N} = 4 supergravity in four dimensions, and show that the minima of the potential describe the same four-dimensional low-energy physics as the worldsheet formulation in terms of asymmetric Gepner models. In this way, we obtain a class of Minkowski vacua of type II string theory which preserve mathcal{N} = 2 supersymmetry. The massless sector consists of mathcal{N} = 2 supergravity coupled to 3 vector multiplets, giving the STU model. In some cases there are additional massless hypermultiplets.
Highlights
Arise at special points in the moduli space of a non-geometric background [2], allowing a complete analysis and important checks on general arguments
[3] K3 mirror-folds with monodromies that, at least when the fiber is compact, break all supersymmetry; in the present work, we consider in contrast monodromies that preserve 8 supersymmetries, i.e. which preserve a quarter of the 32 supersymmetries of the type IIA string, or a half of the 16 supersymmetries of type IIA compactified on K3
In this work we have constructed a new class of N = 2 four-dimensional non-geometric compactifications of type IIA superstring theories, that consist of K3 fibrations over two-tori with non-geometric monodromies which lead in most cases to pure N = 2 STU supergravity with no hypermultiplets at low energies
Summary
The moduli space of two-dimensional conformal field theories defined by quantizing nonlinear sigma models on K3 surfaces is given by [6, 7]: MΣ ∼= O(Γ4,20)\O(4, 20)/O(4) × O(20) ,. The rank of this lattice (i.e. the rank of the corresponding Abelian group) ρ(X), or Picard number, is at least one for any algebraic K3 surface, and its signature is (1, ρ − 1). The moduli space of non-linear sigma-model CFTs on algebraic K3 surfaces with a Picard lattice of Picard number ρ factorizes as [7]: MρΣ ∼= O(T (X))\O(2, 20−ρ)/(O(2)×O(20−ρ)) × O(SQ(X))\O(2, ρ)/(O(2)×O(ρ)). For K3 surfaces the situation is different since (i) all K3 surfaces are diffeomorphic to each other and so have the same Hodge numbers and topology, and (ii) as these manifolds are hyperkahler, the complex structure and complex Kahler moduli are not unambiguously defined. For algebraic K3 surfaces there are two different notions of mirror symmetry that we will review in turn below, and these will both play a role in the construction of the non-geometric automorphisms we use in this paper
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
