Gauge Lattices of Supercritical Heterotic Strings

Supercritical string theories, such as those arising from linear dilaton backgrounds, have notably different massless state symmetry groups from the critical 10-dimensional case. Through the lens of heterotic string theory, we investigate the possible supercritical gauge groups that could play the role of the E₈ × E₈/SO(32) gauge lattice in the critical case, while keeping the theory anomaly-free. We find that, for a Euclidean signature of the compactification lattice, the structure of the massless states in the lowest number of extended dimensions and compact gauge lattice dimensions can be described by the Niemeier lattices.