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Classification of Pati-Salam asymmetric Z2×Z2 heterotic string orbifolds

Luke A. Detraux1,*, Alon E. Faraggi1,†, and Benjamin Percival2,‡

  • *Contact author: ldetraux@liverpool.ac.uk
  • †Contact author: alon.faraggi@liverpool.ac.uk
  • ‡Contact author: b.percival@mmu.ac.uk
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Phys. Rev. D 114, 026002 – Published 1 July, 2026

DOI: https://doi.org/10.1103/75l9-nzd6

Abstract

We develop a systematic classification of asymmetric Z2 orbifold actions in Pati-Salam heterotic string vacua constructed in the free fermionic formulation. Starting from symmetric Z2×Z2 orbifold vacua with an SO(10) grand unified theory (GUT), we allow the Pati-Salam breaking vector to act asymmetrically on the internal degrees of freedom. The asymmetric orbifold action freezes geometrical moduli while inducing doublet-triplet splitting in the untwisted sector. Notably, this doublet-triplet splitting operates for any asymmetric action, including pure asymmetric shifts that preserve all geometric moduli, and is therefore independent of moduli stabilization. Classifying the breaking vector according to its twist action, we find six inequivalent classes of geometric moduli spaces characterized by 12, 8, 4 or 0 real untwisted moduli. Through combining these asymmetric twists with all compatible asymmetric shifts, 24 inequivalent cases are identified and characterized by their residual moduli content and internal Narain lattice. For each case we construct representative basis sets admitting three chiral generations, providing the starting point for further classification within each class. We perform explicit GGSO (Generalized Gliozzi–Scherk–Olive) phase enumerations in representative model classes with 12, 8, 4 and 0 moduli, classify the resulting N=1 and N=0 vacua according to phenomenological criteria and identify exophobic, phenomenologically viable models. We compute the partition function and corresponding one-loop vacuum energy at the free fermionic point in moduli space for each phenomenologically viable model across the four classes. As the number of geometrical moduli decreases, the number of distinct partition functions for these vacua collapses to a small number, reflecting a pronounced degeneracy under GGSO phase variations.

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Phys. Rev. D 114, 026002– Published 1 July, 2026
  • Received 23 April 2026
  • Accepted 8 June 2026
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