An SU(5) Heterotic Standard Model

TL;DR

The paper constructs a concrete heterotic M-theory vacuum on a Calabi–Yau threefold with fundamental group ${\mathbb Z}_2$ that yields precisely the MSSM spectrum with a single Higgs pair in a specific region of moduli space. The observable sector arises from a stable SU(5) bundle built by a nontrivial extension within the spectral-cover/Fourier–Mukai framework, with a Wilson line breaking to ${SU(3)_C \times SU(2)_L \times U(1)_Y}$. A detailed analysis of Chern classes, anomaly cancellation, stability, and cohomology demonstrates that the model contains three generations, no exotics, and a tunable number of Higgs doublet pairs ($n=0,1,2$), with the middle region reproducing the MSSM exactly; the construction relies on tau-invariance and careful control of extension data to realize the desired spectrum. This work advances explicit realizations of MSSM-like vacua in heterotic string theory and highlights the role of moduli in determining Higgs content, with implications for Yukawa structure and low-energy phenomenology.

Abstract

We introduce a new heterotic Standard Model which has precisely the spectrum of the Minimal Supersymmetric Standard Model (MSSM), with no exotic matter. The observable sector has gauge group SU(3) x SU(2) x U(1). Our model is obtained from a compactification of heterotic strings on a Calabi-Yau threefold with Z_2 fundamental group, coupled with an invariant SU(5) bundle. Depending on the region of moduli space in which the model lies, we obtain a spectrum consisting of the three generations of the Standard Model, augmented by 0, 1 or 2 Higgs doublet conjugate pairs. In particular, we get the first compactification involving a heterotic string vacuum (i.e. a {\it stable} bundle) yielding precisely the MSSM with a single pair of Higgs.