The Particle Spectrum of Heterotic Compactifications

TL;DR

This paper develops techniques to compute the particle spectrum in heterotic string compactifications, revealing that the spectrum can change abruptly across moduli space, indicating possible phase transitions.

Contribution

It introduces methods for calculating cohomology of vector bundles on elliptically fibered Calabi-Yau threefolds and shows spectrum jumps in moduli space, suggesting phase transitions.

Findings

Spectrum remains constant at generic moduli points.

Spectrum can jump at co-dimension one or higher loci.

Presented analytic and numerical evidence of spectrum transitions.

Abstract

Techniques are presented for computing the cohomology of stable, holomorphic vector bundles over elliptically fibered Calabi-Yau threefolds. These cohomology groups explicitly determine the spectrum of the low energy, four-dimensional theory. Generic points in vector bundle moduli space manifest an identical spectrum. However, it is shown that on subsets of moduli space of co-dimension one or higher, the spectrum can abruptly jump to many different values. Both analytic and numerical data illustrating this phenomenon are presented. This result opens the possibility of tunneling or phase transitions between different particle spectra in the same heterotic compactification. In the course of this discussion, a classification of SU(5) GUT theories within a specific context is presented.