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Standard Models from Heterotic M-theory

Ron Donagi, Burt A. Ovrut, Tony Pantev, Daniel Waldram

TL;DR

The paper constructs N=1 heterotic M-theory vacua yielding three chiral families and the Standard Model gauge group by compactifying on torus-fibered Calabi–Yau threefolds Z with π1(Z)=Z2. It develops a framework of two-section elliptic fibrations X, a freely acting involution τX, and a spectral-cover description of SU(n) bundles that descend to Z, enabling SU(5) GUTs broken to the SM via a Z2 Wilson line. The authors derive explicit conditions for three families, anomaly cancellation, and five-brane configurations, and provide two concrete examples with base surfaces F2 and dP3 that satisfy all constraints. This work advances realistic brane-world constructions in heterotic M-theory by combining geometric quotienting, Fourier–Mukai spectral data, and Wilson-line breaking. The approach yields calculable five-brane curves and explicit SM-compatible vacua with potential phenomenological relevance.

Abstract

We present a class of N=1 supersymmetric models of particle physics, derived directly from heterotic M-theory, that contain three families of chiral quarks and leptons coupled to the gauge group $SU(3)_C\times SU(2)_{L}\times U(1)_{Y}$. These models are a fundamental form of ``brane-world'' theories, with an observable and hidden sector each confined, after compactification on a Calabi-Yau threefold, to a BPS threebrane separated by a five-dimensional bulk space with size of the order of the intermediate scale. The requirement of three families, coupled to the fundamental conditions of anomaly freedom and supersymmetry, constrains these models to contain additional fivebranes wrapped around holomorphic curves in the Calabi-Yau threefold. These fivebranes ``live'' in the bulk space and represent new, non-perturbative aspects of these particle physics vacua. We discuss, in detail, the relevant mathematical structure of a class of torus-fibered Calabi-Yau threefolds with non-trivial first homotopy groups and construct holomorphic vector bundles over such threefolds, which, by including Wilson lines, break the gauge symmetry to the standard model gauge group. Rules for constructing phenomenological particle physics models in this context are presented and we give a number of explicit examples.

Standard Models from Heterotic M-theory

TL;DR

The paper constructs N=1 heterotic M-theory vacua yielding three chiral families and the Standard Model gauge group by compactifying on torus-fibered Calabi–Yau threefolds Z with π1(Z)=Z2. It develops a framework of two-section elliptic fibrations X, a freely acting involution τX, and a spectral-cover description of SU(n) bundles that descend to Z, enabling SU(5) GUTs broken to the SM via a Z2 Wilson line. The authors derive explicit conditions for three families, anomaly cancellation, and five-brane configurations, and provide two concrete examples with base surfaces F2 and dP3 that satisfy all constraints. This work advances realistic brane-world constructions in heterotic M-theory by combining geometric quotienting, Fourier–Mukai spectral data, and Wilson-line breaking. The approach yields calculable five-brane curves and explicit SM-compatible vacua with potential phenomenological relevance.

Abstract

We present a class of N=1 supersymmetric models of particle physics, derived directly from heterotic M-theory, that contain three families of chiral quarks and leptons coupled to the gauge group . These models are a fundamental form of ``brane-world'' theories, with an observable and hidden sector each confined, after compactification on a Calabi-Yau threefold, to a BPS threebrane separated by a five-dimensional bulk space with size of the order of the intermediate scale. The requirement of three families, coupled to the fundamental conditions of anomaly freedom and supersymmetry, constrains these models to contain additional fivebranes wrapped around holomorphic curves in the Calabi-Yau threefold. These fivebranes ``live'' in the bulk space and represent new, non-perturbative aspects of these particle physics vacua. We discuss, in detail, the relevant mathematical structure of a class of torus-fibered Calabi-Yau threefolds with non-trivial first homotopy groups and construct holomorphic vector bundles over such threefolds, which, by including Wilson lines, break the gauge symmetry to the standard model gauge group. Rules for constructing phenomenological particle physics models in this context are presented and we give a number of explicit examples.

Paper Structure

This paper contains 15 sections, 130 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Fibered Calabi--Yau threefolds with non-trivial $\pi_1$
  3. Torus and elliptic fibrations
  4. Involutions and the construction of $Z$ with $\pi_1(Z)={\mathbb{Z}}_2$
  5. Structure of $X$
  6. Classes, effective curves and the Chern class $c_{2}(TX)$
  7. Holomorphic vector bundles on fibered Calabi--Yau threefolds
  8. T-duality and the spectral construction
  9. Bundles on $X$ and the form of the spectral data
  10. Vector Bundles on $Z=X/\tau_X$
  11. Rules for Realistic Particle Physics Vacua
  12. Three Family Models
  13. Example 1: $B=F_2$
  14. Example 2: $B=dP_{3}$
  15. Conclusions

Figures (3)

  • Figure 1: Heterotic M-theory brane-world
  • Figure 2: Structure of $X$
  • Figure 3: The Fourier--Mukai T-duality transform