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Stability of the Minimal Heterotic Standard Model Bundle

Volker Braun, Yang-Hui He, Burt A. Ovrut

TL;DR

<3-5 sentence high-level summary>

Abstract

The observable sector of the "minimal heterotic standard model" has precisely the matter spectrum of the MSSM: three families of quarks and leptons, each with a right-handed neutrino, and one Higgs-Higgs conjugate pair. In this paper, it is explicitly proven that the SU(4) holomorphic vector bundle leading to the MSSM spectrum in the observable sector is slope-stable.

Stability of the Minimal Heterotic Standard Model Bundle

TL;DR

<3-5 sentence high-level summary>

Abstract

The observable sector of the "minimal heterotic standard model" has precisely the matter spectrum of the MSSM: three families of quarks and leptons, each with a right-handed neutrino, and one Higgs-Higgs conjugate pair. In this paper, it is explicitly proven that the SU(4) holomorphic vector bundle leading to the MSSM spectrum in the observable sector is slope-stable.

Paper Structure

This paper contains 18 sections, 1 theorem, 61 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The Calabi-Yau Manifold
  3. Double Fibration
  4. Topology
  5. Visible Bundle
  6. Construction of the Bundle
  7. Non-Trivial Extensions
  8. Low-Energy Spectrum
  9. Slope-Stability
  10. Conditions for Stability
  11. Kähler Cone Substructure
  12. Hidden Sector
  13. Serre Construction
  14. General Construction
  15. Ideal Sheaves
  16. ...and 3 more sections

Key Result

Proposition 1

If all line bundles $\mathcal{O}_{{\widetilde{X}}}(a_1\tau_1+a_2\tau_2+b\phi)$ with have negative slope, then the vector bundle ${\widetilde{\mathcal{V}_{}}}$, eq. eq:Vdef, is equivariantly stable.

Figures (1)

  • Figure 1: Map projection of the unit sphere intersecting the Kähler cone, that is, the positive octant in $H^2({\widetilde{X}},\mathbb{R})\simeq \mathbb{R}^3$. The rank $4$ bundle ${\widetilde{\mathcal{V}_{}}}$ is stable inside the black triangular region $\mathcal{K}^s$. In the white region $\mathcal{K}^B$ the Bogomolov inequality allows an $\mathcal{N}=1$ hidden sector, see Section \ref{['sec:hidden']}.

Theorems & Definitions (1)

  • Proposition 1