Moduli Dependent Spectra of Heterotic Compactifications

TL;DR

This paper develops explicit methods to compute the cohomology of vector bundles on elliptically fibered Calabi-Yau threefolds, revealing how the particle spectrum in heterotic compactifications varies with bundle moduli.

Contribution

It introduces explicit computational techniques for cohomology in heterotic compactifications and demonstrates moduli-dependent spectrum variations with concrete examples.

Findings

Spectrum depends on vector bundle moduli

Cohomology jumps on subspaces of moduli space

Explicit example for SU(5) GUT vacuum

Abstract

Explicit methods are presented for computing the cohomology of stable, holomorphic vector bundles on elliptically fibered Calabi-Yau threefolds. The complete particle spectrum of the low-energy, four-dimensional theory is specified by the dimensions of specific cohomology groups. The spectrum is shown to depend on the choice of vector bundle moduli, jumping up from a generic minimal result to attain many higher values on subspaces of co-dimension one or higher in the moduli space. An explicit example is presented within the context of a heterotic vacuum corresponding to an SU(5) GUT in four-dimensions.