Exploring the landscape of CHL strings on Td

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 <= 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 of lattices into the dual of II(2). Our results easily generalize to d > 2.

Automated summary

This study focuses on compactifications of the heterotic string on special T-d/Z(2) orbifolds, revealing properties of string models and gauge groups; systematic exploration of the moduli space using computer algorithms, identifying points where the U(1)(d+8) enhances to a non-Abelian gauge group; findings on group structures in specific dimensions.