The Spectra of Heterotic Standard Model Vacua

TL;DR

This paper develops a formalism to compute the massless spectrum of heterotic string vacua with realistic features, including standard model gauge group and three families, by analyzing sheaf cohomology on specific Calabi-Yau threefolds.

Contribution

It introduces a new methodology for calculating the sheaf cohomology and spectrum of heterotic string vacua with SU(5) bundles on torus-fibered Calabi-Yau threefolds with Z_2 symmetry.

Findings

Computed the massless spectrum for a class of heterotic vacua.

Established a method for analyzing sheaf cohomology with Z_2 action.

Identified conditions for realistic low-energy theories.

Abstract

A formalism for determining the massless spectrum of a class of realistic heterotic string vacua is presented. These vacua, which consist of SU(5) holomorphic bundles on torus-fibered Calabi-Yau threefolds with fundamental group Z_2, lead to low energy theories with standard model gauge group (SU(3)_C x SU(2)_L x U(1)_Y)/Z_6 and three families of quarks and leptons. A methodology for determining the sheaf cohomology of these bundles and the representation of Z_2 on each cohomology group is given. Combining these results with the action of a Z_2 Wilson line, we compute, tabulate and discuss the massless spectrum.