A Standard Model from the E8 x E8 Heterotic Superstring

TL;DR

This paper constructs a heterotic string model with the MSSM spectrum on a Calabi-Yau manifold, detailing vector bundle formulation, cohomology computation, and particle spectrum analysis.

Contribution

It introduces a method to formulate stable holomorphic bundles with specific structure groups on Calabi-Yau threefolds and computes the low-energy spectrum explicitly.

Findings

MSSM spectrum achieved with additional Higgs pair

Explicit cohomology computation method developed

Low-energy particle spectrum determined

Abstract

In a previous paper, we introduced a heterotic standard model and discussed its basic properties. This vacuum has the spectrum of the MSSM with one additional pair of Higgs-Higgs conjugate fields and a small number of uncharged moduli. In this paper, the requisite vector bundles are formulated; specifically, stable, holomorphic bundles with structure group SU(N) on smooth Calabi-Yau threefolds with Z_3 x Z_3 fundamental group. A method for computing bundle cohomology is presented and used to evaluate the cohomology groups of the standard model bundles. It is shown how to determine the Z_3 x Z_3 action on these groups. Finally, using an explicit method of "doublet-triplet splitting", the low-energy particle spectrum is computed.