Quasicrystalline string landscape

In this work, we investigate a largely unexplored nongeometric 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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mn>4</a:mn><a:mo>≤</a:mo><a:mi>D</a:mi><a:mo>≤</a:mo><a:mn>6</a:mn></a:math> and with <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mn>4</c:mn><c:mo>≤</c:mo><c:mi>Q</c:mi><c:mo>≤</c:mo><c:mn>16</c:mn></c:math> supercharges, leading to novel theories, including theories with large quantum symmetries at all points in the moduli space. We anticipate that these constructions will have many applications, and in subsequent work, we apply these techniques to construct new nonsupersymmetric tachyon-free models. Similarly, these constructions can lead to constructing exotic matter representations in the string landscape.