Little heterotic strings

TL;DR

This paper explores specific heterotic string models involving orbifolds and shifts, analyzing their spectrum, consistency, and dualities, with implications for string theory and supersymmetry.

Contribution

It introduces new heterotic string models with unique orbifold projections affecting the spectrum and discusses their mathematical consistency and duality properties.

Findings

Projection can remove the graviton from the spectrum

Massive spectrum exhibits flipped spin-statistics assignments

Models maintain one- and multi-loop amplitude consistency

Abstract

We discuss toroidal orbifolds of the E8XE8 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 nonzero temperature is briefly discussed.