Superstring standard model from Z_{12-I} orbifold compactification with and without exotics, and effective R-parity

TL;DR

This work constructs a string-theoretic supersymmetric Standard Model from a ${\bf Z}_{12-I}$ orbifold of the heterotic string, yielding three chiral families and Higgs content within a gauge group that includes additional ${U(1)}$ factors and a hidden sector. By examining two hypercharge embeddings (Model E with exotics and Model S with no exotics), the authors show how a viable vacuum can give heavy masses to all exotics via neutral-singlet VEVs and realize an effective R-parity that stabilizes the LSP as a dark matter candidate. They demonstrate explicit mass matrices for quarks and leptons, discuss the generation of the MSSM $\mu$ term, and analyze $D$- and $F$-flat directions, anomaly cancellation via Green–Schwarz, and the presence of an exphoton from a massless ${U(1)}_6$. The study provides a concrete realization of an MSSM-like vacuum in string theory, with controlled proton decay operators and a framework for embedding R-parity in a gauged symmetry, highlighting both viable phenomenology and remaining questions about vacuum selection and dynamics in the full theory.

Abstract

We construct a supersymmetric standard model in the context of the $Z_{12-I}$ orbifold compactification of the heterotic string theory. The gauge group is $SU(3)_c\times SU(2)_L\times U(1)_Y\times U(1)^4\times[SO(10)\times U(1)^3]'$. We obtain three chiral families, $3\times\{Q,d^c,u^c,L,e^c,ν^c\}$, and Higgs doublets. There are numerous neutral singlets many of which can have VEVs so that low energy phenomenology on Yukawa couplings can be satisfied. In one assignment (Model E) of the electroweak hypercharge, we obtain the string scale value of $sin^2θ_W^0={3/8}$ and another exactly massless {\it exphoton} (in addition to the photon) coupling to exotic particles only. There are color triplet and anti-triplet exotics, $α$ and $\barα$, $SU(2)_L$ doublet exotics, $δ$ and $\barδ$, and $SU(3)_c\times SU(2)_L$ singlet but $Y={2/3},-{1/3},-{2/3},{1/3}$ exotics, $ξ,η,\barξ, \barη$. We show that all these vector-like exotics achieve heavy masses by appropriate VEVs of neutral singlets. One can find an effective R-parity between light (electroweak scale) particles so that proton and the LSP can live sufficiently long. In another assignment (Model S) of the electroweak hypercharge, there does not appear any exotic particle but $sin^2θ_W^0={3/14}$.