Exploring the landscape of CHL strings on T^d

Understand

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}.