Tracing symmetries and their breakdown through phases of heterotic (2,2) compactifications

  • Michael Blaszczyk
  • Paul-Konstantin OehlmannEmail author
Open Access
Regular Article - Theoretical Physics


We are considering the class of heterotic \( \mathcal{N}=\left(2,2\right) \) 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 \( \mathcal{N}=1 \), 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 \( {\mathrm{\mathbb{Z}}}_3 \) 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 \( {\mathrm{\mathbb{Z}}}_3\times {\mathrm{\mathbb{Z}}}_{3,\mathrm{free}} \) orbifold regime.


Extended Supersymmetry Superstrings and Heterotic Strings Discrete Symmetries Superstring Vacua 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Johannes-Gutenberg-UniversitätMainzGermany
  2. 2.Bethe Center for Theoretical Physics, Physikalisches Institut der Universität BonnBonnGermany

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