Exploring the landscape of CHL strings on T^d

Abstract

Compactifications of the heterotic string on special T^d/Z_2 orbifolds realize a landscape of string models with 16 supercharges and a gauge group on the left-moving sector of reduced rank d+8. The momenta of untwisted and twisted states span a lattice known as the Mikhailov lattice II_{(d)}, which is not self-dual for d > 1. By using computer algorithms which exploit the properties of lattice embeddings, we perform a systematic exploration of the moduli space for d=1 and 2, and give a list of maximally enhanced points where the U(1)^{d+8} enhances to a rank d+8 non-Abelian gauge group. For d = 1, these groups are simply-laced and simply-connected, and in fact can be obtained from the Dynkin diagram of E_{10}. For d = 2 there are also symplectic and doubly-connected groups. For the latter we find the precise form of their fundamental groups from embeddings ofof lattices into the dual of II_{(2)}. Our results easily generalize to d > 2.

arXiv comment65 pages. v2: corrected global groups

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• New Supersymmetric String Theories from Discrete Theta Angles
• Quantum Gravity Bounds on N=1 Effective Theories in Four Dimensions
• Freezing of Gauge Symmetries in the Heterotic String on $T^4$
• Bordism for the 2-group symmetries of the heterotic and CHL strings
• Unifying the 6D $\mathcal{N}=(1,1)$ String Landscape
• New Supersymmetric String Moduli Spaces from Frozen Singularities
• Flat equivariant gerbes: holonomies and dualities
• Affine Algebras at Infinite Distance Limits in the Heterotic String
• Open Strings in IIB Orientifold Reductions
• Consistency of eight-dimensional supergravities: Anomalies, Lattices and Counterterms
• $E_9$ symmetry in the Heterotic String on $S^1$ and the Weak Gravity Conjecture