A Standard Model from the E8 x E8 Heterotic Superstring

TL;DR

This work constructs a concrete heterotic-string vacuum with an MSSM-like observable sector via stable holomorphic SU(4) bundles on a Calabi–Yau threefold with fundamental group $\mathbb{Z}_3\times\mathbb{Z}_3$. By computing bundle cohomologies on the covering space and implementing a $\mathbb{Z}_3\times\mathbb{Z}_3$ action together with Wilson lines, the authors obtain three chiral generations and two Higgs doublets without exotics, realized through a doublet–triplet splitting mechanism. The paper presents an explicit observable-sector bundle tildeV with $c_1=0$, $c_3=-54$, and cohomology data that yield $h^1(tildeX, tildeV)^G=3$ and $h^1(tildeX, wedge^2 tildeV)^G=2$, along with two consistent hidden-sector scenarios: (i) strong coupling with bulk five-branes giving $E_7\times U(6)$ and no hidden matter, and (ii) weak coupling without five-branes leading to Spin(12) with two exotic $\mathbf{12}$ multiplets.

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.