A Heterotic Standard Model

TL;DR

The work seeks realistic $N=1$ heterotic vacua whose observable sector matches the Standard Model extended by a gauged $U(1)_{B-L}$ and includes three generations with right-handed neutrinos. It constructs a stable, holomorphic vector bundle $V$ with structure group $SU(4)$ on a Calabi–Yau threefold $X$ with $\,\pi_1(X)=\mathbb{Z}_3\times\mathbb{Z}_3$, using an equivariant lift $\widetilde{V}$ on $\widetilde{X}$ and a Wilson line with $\mathrm{Hol}(W)=\mathbb{Z}_3\times\mathbb{Z}_3$ to break $Spin(10)$ to $SU(3)_C\times SU(2)_L\times U(1)_Y\times U(1)_{B-L}$. The observable sector spectrum includes three quark/lepton families, each with a right-handed neutrino, two Higgs–Higgs conjugate pairs, and no exotic matter, together with a small set of uncharged moduli. In the strong coupling regime the hidden sector is $E_7\times U(6)$ with no matter and potential gaugino condensation; in the weakly coupled regime the hidden sector is $Spin(12)$ with a small amount of exotic $\mathbf{12}$ matter, and anomaly cancellation constrains the visible and hidden bundles via the five-brane class $[\mathcal{W}]$. This class of vacua, labeled a heterotic standard model, demonstrates a realistic low-energy content in a string framework, highlights the phenomenological relevance of spontaneously broken $U(1)_{B-L}$ and two Higgs conjugate pairs, and suggests natural suppression of nucleon decay.

Abstract

Within the context of the E_8 x E_8 heterotic superstring compactified on a smooth Calabi-Yau threefold with an SU(4) gauge instanton, we show the existence of simple, realistic N=1 supersymmetric vacua that are compatible with low energy particle physics. The observable sector of these vacua has gauge group SU(3)_C x SU(2)_L x U(1)_Y x U(1)_{B-L}, three families of quarks and leptons, each with an additional right-handed neutrino, two Higgs-Higgs conjugate pairs, a small number of uncharged moduli and no exotic matter. The hidden sector contains non-Abelian gauge fields and moduli. In the strong coupling case there is no exotic matter, whereas for weak coupling there are a small number of additional matter multiplets in the hidden sector. The construction exploits a mechanism for ``splitting'' multiplets. The minimal nature and rarity of these vacua suggest the possible theoretical and experimental relevance of spontaneously broken U(1)_{B-L} gauge symmetry and two Higgs-Higgs conjugate pairs. The U(1)_{B-L} symmetry helps to naturally suppress the rate of nucleon decay.