Abstract
Phenomenological explorations of heterotic strings have conventionally focused primarily on the E8×E8 theory. We consider smooth compactifications of all three ten-dimensional heterotic theories to exhibit the many similarities between the non-supersymmetric SO(16)×SO(16) theory and the related supersymmetric E8×E8 and SO(32) theories. In particular, we exploit these similarities to determine the bosonic and fermionic spectra of Calabi-Yau compactifications with line bundles of the non-supersymmetric string. We use elements of four-dimensional supersymmetric effective field theory to characterize the non-supersymmetric action at leading order and determine the Green-Schwarz induced axion couplings. Using these methods we construct a non-supersymmetric Standard Model(SM)-like theory. In addition, we show that it is possible to obtain SM-like models from the standard embedding using at least an order four Wilson line. Finally, we make a proposal of the states that live on five-branes in the SO(16)×SO(16) theory and find under certain assumptions the surprising result that anomaly factorization only admits at most a single brane solution.
Highlights
One may wonder about the consequences for string theory if supersymmetry will not be found at the LHC or possible future accelerators
The statement that string theory requires target space supersymmetry is false: as had been realized, essentially during the time that string theory was first considered as a unified framework of all particles and interactions, it is possible to construct consistent string theories without space-time supersymmetry
While there are potential solutions known for the last two points (gauge coupling unification could be achived via Kaluza-Klein threshold corrections and string theory predicts many extra particles which might serve as dark matter), a natural solution to the hierarchy problem in theories without supersymmetry is currently not known to the authors
Summary
Consistent string theories are characterized as string constructions that have low energy spectra which are free of anomalies and tachyons and have a modular invariant one-loop partition function. In ten dimensions there are three consistent heterotic string theories in this sense: the two that are most commonly studied, the E8×E8 and SO(32) theories, are supersymmetric in target space. The third theory with gauge group SO(16)×SO(16) is non-supersymmetric. It is common to distinguish the three heterotic theories by their ten-dimensional gauge group, as will be done here as well
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