Little heterotic strings

We discuss toroidal orbifolds of the E ₈×E ₈ heterotic string, in which the free-fermionic Higgs–matter splitting is implemented by a shift in the internal lattice coupled with the fermion numbers of the gauge degrees of freedom. We consider models in which some choices of the orbifold result in the projection of the graviton. In the models that we consider the projection also results in flipping the spin–statistics assignments in the massive string spectrum, whereas the massless spectrum retains the conventional spin–statistics assignments. We argue that the partition functions are mathematically consistent for one- and multi-loop amplitudes, owning to the existence of supersymmetry in the spectrum. A duality between different models at non-zero temperature is briefly discussed.