More on 8d non-supersymmetric branes and heterotic strings

We determine the maximal gauge groups arising in E₈ heterotic string theory on T². Our analysis proceeds along two approaches. First, we start the moduli space of the supersymmetric heterotic string theory on T² focusing on points of maximal gauge enhancement. At these special points, the charge lattice can exhibit a Z₂ outer automorphism corresponding to the bulk gauge symmetry. By orbifolding the worldsheet theory by it with the fermion parity, we obtain the maximal gauge group of the E₈ theory. Second, we directly study the toroidal compactification of 10d E₈ heterotic string. Both approaches agree, yielding a classification of 22 maximal gauge groups. For each case, we present the corresponding massless spectrum. In light of the no global symmetry/cobordism conjecture in quantum gravity, our result also offer a classification of non-supersymmetric branes in 8d supersymmetric heterotic string theories.