The Quasicrystalline String Landscape

TL;DR

This paper explores a new class of non-geometric string compactifications called quasicrystalline orbifolds, classifying their structures and revealing their potential for novel theories with large quantum symmetries and applications in non-geometric models.

Contribution

It completes the classification of quasicrystalline Narain lattices and applies this to construct new supersymmetric and non-supersymmetric string models with exotic features.

Findings

Classified and constructed quasicrystalline Narain lattices.

Discovered theories with large quantum symmetries across moduli space.

Developed techniques for non-geometric F-theory and tachyon-free models.

Abstract

In this work we investigate a largely unexplored non-geometric corner of the string landscape: the quasicrystalline orbifolds. These exist at special points of the Narain moduli leading to frozen moduli and large quantum symmetries. Here we complete the classification and construction of quasicrystalline Narain lattices and use this to explore supersymmetric compactifications in $4\leq D\leq 6$ and with $4\leq Q\leq 16$ supercharges, leading to novel theories including theories with large quantum symmetries at all points in the moduli space. We anticipate these constructions will have many applications and in subsequent papers we apply these techniques to construct non-geometric F-theory models as well as new non-supersymmetric tachyon free models. Similarly these constructions can lead to constructing exotic matter representations in the string landscape.