Abstract
We are considering the class of heterotic N = 2 2 $$ \mathcal{N}=\left(2,2\right) $$ Landau-Ginzburg orbifolds with 9 fields corresponding to A 1 9 Gepner models. We classify all of its Abelian discrete quotients and obtain 152 inequivalent models closed under mirror symmetry with N = 1 $$ \mathcal{N}=1 $$ , 2 and 4 supersymmetry in 4D. We compute the full massless matter spectrum at the Fermat locus and find a universal relation satisfied by all models. In addition we give prescriptions of how to compute all quantum numbers of the 4D states including their discrete R-symmetries. Using mirror symmetry of rigid geometries we describe orbifold and smooth Calabi-Yau phases as deformations away from the Landau-Ginzburg Fermat locus in two explicit examples. We match the non-Fermat deformations to the 4D Higgs mechanism and study the conservation of R-symmetries. The first example is a ℤ 3 $$ {\mathrm{\mathbb{Z}}}_3 $$ orbifold on an E6 lattice where the R-symmetry is preserved. Due to a permutation symmetry of blow-up and torus Kähler parameters the R-symmetry stays conserved also in the smooth Calabi-Yau phase. In the second example the R-symmetry gets broken once we deform to the geometric ℤ 3 × ℤ 3 , free $$ {\mathrm{\mathbb{Z}}}_3\times {\mathrm{\mathbb{Z}}}_{3,\mathrm{free}} $$ orbifold regime.