Exploring the landscape of heterotic strings on T^d

Understand

Compactifications of the heterotic string on T^d are the simplest, yet rich enough playgrounds to uncover swampland ideas: the U(1)^{d+16} left-moving gauge symmetry gets enhanced at special points in moduli space only to certain groups.

• We state criteria, based on lattice embedding techniques, to establish whether a gauge group is realized or not.
• For generic d, we further show how to obtain the moduli that lead to a given gauge group by modifying the method of deleting nodes in the extended Dynkin diagram of the Narain lattice II_{1,17}.
• More general algorithms to explore the moduli space are also developed.