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From strings to the MSSM

Hans Peter Nilles, Saul Ramos-Sanchez, Michael Ratz, Patrick K. S. Vaudrevange

TL;DR

The paper surveys embedding the MSSM into string theory using heterotic orbifolds with local GUTs, emphasizing the $\mathbb{Z}_{6}$-II and $\mathbb{Z}_{12}$-I constructions. It argues that near-orbifold points in moduli space and grand-unified structures help obtain three chiral generations, exact MSSM spectrum below $M_{\mathrm{GUT}}$, $R$-parity, and hierarchical Yukawa couplings. The authors perform a Mini-Landscape scan showing about $0.7\%$ of models yield MSSM-like spectra with viable decoupling of exotics, and discuss features such as the $\mu$-term generation and see-saw neutrino masses. They also discuss orbifold GUT limits, connections to Calabi–Yau compactifications, and implications for gauge-coupling unification and proton stability.

Abstract

We review recent progress in embedding the supersymmetric standard model into string theory. We discuss how, with the incorporation of certain aspects of grand unification, a search strategy can be developed that allows to efficiently find rather large numbers of promising string vacua. Global string-derived models with the following features are discussed: (i) exact MSSM spectrum below the unification scale; (ii) R parity; (iii) hierarchical Yukawa couplings with non-trivial mixing; (iv) solution to the mu problem; (v) see-saw suppressed neutrino masses.

From strings to the MSSM

TL;DR

The paper surveys embedding the MSSM into string theory using heterotic orbifolds with local GUTs, emphasizing the -II and -I constructions. It argues that near-orbifold points in moduli space and grand-unified structures help obtain three chiral generations, exact MSSM spectrum below , -parity, and hierarchical Yukawa couplings. The authors perform a Mini-Landscape scan showing about of models yield MSSM-like spectra with viable decoupling of exotics, and discuss features such as the -term generation and see-saw neutrino masses. They also discuss orbifold GUT limits, connections to Calabi–Yau compactifications, and implications for gauge-coupling unification and proton stability.

Abstract

We review recent progress in embedding the supersymmetric standard model into string theory. We discuss how, with the incorporation of certain aspects of grand unification, a search strategy can be developed that allows to efficiently find rather large numbers of promising string vacua. Global string-derived models with the following features are discussed: (i) exact MSSM spectrum below the unification scale; (ii) R parity; (iii) hierarchical Yukawa couplings with non-trivial mixing; (iv) solution to the mu problem; (v) see-saw suppressed neutrino masses.

Paper Structure

This paper contains 18 sections, 30 equations, 10 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Supersymmetry and grand unified structures
  3. Orbifold compactifications
  4. Simple ways of envisaging orbifolds
  5. Gauge group topography
  6. Local grand unification
  7. Orbifold vacua
  8. Properties of the effective field theories derived from orbifolds
  9. Approaching the MSSM
  10. String derived orbifold GUTs
  11. MSSM from the heterotic string
  12. The heterotic Mini-Landscape
  13. How good are the Mini-Landscape models?
  14. MSSM-like models from the $\boldsymbol{\mathbbm{Z}_{12}}$-I orbifolds
  15. Comments on the SO(32) heterotic string
  16. ...and 3 more sections

Figures (10)

  • Figure 1: $\Lambda_{\mathrm{G}_{2}\times\mathrm{SU}(3)\times\mathrm{SO}(4)}$ and $\mathbbm{Z}_{6}$ fixed points.
  • Figure 2: The $\mathbbm{Z}_{2}$ orbifold of a torus based on a hexagonal lattice can be envisaged as a tetrahedron.
  • Figure 3: Gauge group topography. At different fixed points (corners of the tetrahedron), $\mathrm{E}_{8}$ gets broken to different subgroups ($\mathrm{U}(1)$ factors are suppressed). At the edges we display the intersection of the two local gauge groups realized at the corners.
  • Figure 4: A $\mathbbm{Z}_{2}$ orbifold in two steps. One compactifies first on a torus with a discrete Wilson line $W$. Then, modding out a $\mathbbm{Z}_{2}$ symmetry of this torus leads to an orbifold in which the local shifts differ by $W$.
  • Figure 5: Different types of supersymmetric vacua of a given orbifold model.
  • ...and 5 more figures