Abstract
The strategy for assigning ${\mathbf{Z}}_{4R}$ parity in the string compactification is presented. For the visible sector, an anti-SU(5) [flipped-SU(5)] grand unification (GUT) model with three families is used to reduce the number of representations compared to the number in the minimal supersymmetric standard models. The SO(32) heterotic string is used to allow a large non-Abelian gauge group $\mathrm{SU}(N)$, $N\ensuremath{\ge}9$, for the hidden sector such that the number of extra U(1) factors is small. A discrete subgroup of the gauge U(1)'s is defined as the ${\mathbf{Z}}_{4R}$ parity. Spontaneous symmetry breaking of anti-SU(5) GUT is achieved by the vacuum expectation values of two index antisymmetric tensor Higgs fields ${\mathbf{10}}_{+1}$ and ${\overline{\mathbf{10}}}_{\ensuremath{-}1}$ that led to our word ``anti-SU(5).'' In the illustrated example, the multiplicity 3 in one twisted sector allows the permutation symmetry ${S}_{3}$ that leads us to select the third family members and one MSSM pair of the Higgs quintets.
Highlights
Grand unified theories (GUTs) attracted a great deal of attention ethetically because they provided unification of gauge couplings and charge quantization [1,2,3]
There seems to be a fundamental reason leading to GUTs even at the standard model (SM) level
In this paper we study the R parity assignment for a family-GUT from string compactification
Summary
Grand unified theories (GUTs) attracted a great deal of attention ethetically because they provided unification of gauge couplings and charge quantization [1,2,3]. The standard-like models from string have been the main focus of string compactification for the ultraviolet completion of the SM toward the minimal supersymmetric standard model (MSSM) or supersymmetric standard models (SSMs) in the last several decades [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34] These models use the chiral spectrum from the level–1 construction which leads to unification of gauge couplings [35].
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