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The Heterotic Road to the MSSM with R parity

Oleg Lebedev, Hans Peter Nilles, Stuart Raby, Saul Ramos-Sanchez, Michael Ratz, Patrick K. S. Vaudrevange, Akin Wingerter

TL;DR

This work extends a heterotic Z6-II orbifold search to identify numerous vacua that realize the MSSM spectrum with exact R-parity and vector-like exotics decoupled along D-flat directions. By enforcing a B−L–based family reflection symmetry and carefully analyzing F=0/D=0 conditions, the authors isolate 15 models with exact R-parity and viable top Yukawas, among them two explicit benchmark vacua with realistic Yukawa textures and See-Saw neutrino masses. They demonstrate that the μ-term can be correlated with the vacuum expectation value of the superpotential, potentially yielding a Minkowski-like vacuum with small gravitino mass in Model 1, while Model 2 presents different Higgs mixing and mass-generation patterns. The results illustrate that a non-negligible fraction of heterotic vacua can mimic MSSM physics, while also highlighting challenges such as dimension-5 proton decay operators and the need for moduli stabilization and SUSY-breaking mechanisms. Overall, the paper provides concrete string-theoretic pathways to MSSM-like physics with robust R-parity, along with detailed analyses of exotics, Yukawa structures, and neutrino masses in explicit vacua.

Abstract

In a previous paper, referred to as a "Mini-Landscape" search, we explored a "fertile patch" of the heterotic landscape based on a Z6-II orbifold with SO(10) and E6 local GUT structures. In the present paper we extend this analysis. We find many models with the minimal supersymmetric standard model spectra and an exact R parity. In all of these models, the vector-like exotics decouple along D flat directions. We present two "benchmark" models which satisfy many of the constraints of a realistic supersymmetric model, including non-trivial Yukawa matrices for 3 families of quarks and leptons and Majorana neutrino masses for right-handed neutrinos with non-trivial See-Saw masses for the 3 light neutrinos. In an appendix we comment on the important issue of string selection rules and in particular the so-called "gamma-rule".

The Heterotic Road to the MSSM with R parity

TL;DR

This work extends a heterotic Z6-II orbifold search to identify numerous vacua that realize the MSSM spectrum with exact R-parity and vector-like exotics decoupled along D-flat directions. By enforcing a B−L–based family reflection symmetry and carefully analyzing F=0/D=0 conditions, the authors isolate 15 models with exact R-parity and viable top Yukawas, among them two explicit benchmark vacua with realistic Yukawa textures and See-Saw neutrino masses. They demonstrate that the μ-term can be correlated with the vacuum expectation value of the superpotential, potentially yielding a Minkowski-like vacuum with small gravitino mass in Model 1, while Model 2 presents different Higgs mixing and mass-generation patterns. The results illustrate that a non-negligible fraction of heterotic vacua can mimic MSSM physics, while also highlighting challenges such as dimension-5 proton decay operators and the need for moduli stabilization and SUSY-breaking mechanisms. Overall, the paper provides concrete string-theoretic pathways to MSSM-like physics with robust R-parity, along with detailed analyses of exotics, Yukawa structures, and neutrino masses in explicit vacua.

Abstract

In a previous paper, referred to as a "Mini-Landscape" search, we explored a "fertile patch" of the heterotic landscape based on a Z6-II orbifold with SO(10) and E6 local GUT structures. In the present paper we extend this analysis. We find many models with the minimal supersymmetric standard model spectra and an exact R parity. In all of these models, the vector-like exotics decouple along D flat directions. We present two "benchmark" models which satisfy many of the constraints of a realistic supersymmetric model, including non-trivial Yukawa matrices for 3 families of quarks and leptons and Majorana neutrino masses for right-handed neutrinos with non-trivial See-Saw masses for the 3 light neutrinos. In an appendix we comment on the important issue of string selection rules and in particular the so-called "gamma-rule".

Paper Structure

This paper contains 26 sections, 113 equations, 2 figures, 5 tables.

Table of Contents

  1. Introduction
  2. "Mini-Landscape" search strategy Lebedev:2006kn: Local GUTs
  3. Decoupling exotics
  4. Road to the MSSM
  5. Constraints
  6. Approaching the MSSM
  7. Two "Benchmark" models with R-parity
  8. Model 1
  9. Model 1, vacuum configuration A
  10. Model 1, vacuum configuration B
  11. Model 2
  12. Conclusions and Discussion
  13. Physical states and string selection rules
  14. Physical states
  15. String selection rules
  16. ...and 11 more sections

Figures (2)

  • Figure 1: $\mathrm{G}_{2}\times\mathrm{SU}(3)\times\mathrm{SO}(4)$ torus lattice of a $\mathbbm{Z}_{6}$-II orbifold. Possible Wilson lines are denoted by $W_3$, $W_2$ and $W_2'$. The fixed points in the figure are those of the $T_1$ twisted sector.
  • Figure 2: Illustration of the $\gamma$--factor. The fixed point associated with the space group element $g_2=(\theta,\,e_3)$ is invariant under $(\theta,\,e_3)$, but transforms into equivalent fixed points outside the fundamental domain under $h=(\theta,0)$. To form an eigenstate of $(\theta,0)$, one needs to build linear combinations of the equivalent fixed points. The corresponding eigenvalues can be $1, \mathrm{e}^{\pm 2\pi \mathrm{i}/3}$.