Classification of Pati--Salam Asymmetric ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ Heterotic String Orbifolds

Abstract

We develop a systematic classification of asymmetric ${\mathbb{Z}}_2$ orbifold actions in Pati-Salam heterotic string vacua constructed in the free fermionic formulation. Starting from symmetric ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ orbifold vacua with an $SO(10)$ GUT, we allow the Pati--Salam breaking vector to act asymmetrically on the internal degrees of freedom. The asymmetric orbifold action freezes geometrical moduli whilst 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 stabilisation. Classifying the breaking vector according to its twist action, we find six inequivalent classes of geometric moduli spaces characterised 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 characterised 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 $\mathcal{N}=1$ and $\mathcal{N}=0$ 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.

arXiv comment64 pages, 1 figure, 16 tables

References in corpus (43)

• Building a Better Racetrack
• Doubled Geometry and T-Folds
• Construction of Realistic Standard--like Models in the Free Fermionic Superstring Formulation
• Perturbative and Non-Perturbative Partial Supersymmetry Breaking; N=4 -> N=2 -> N=1
• String derived MSSM and M-theory Unification
• Towards a Non-Supersymmetric String Phenomenology
• Vacuum Energy Cancellation in a Non-supersymmetric String
• N=1 supersymmetric SU(4)xSU(2)LxSU(2)R effective theory from the weakly coupled heterotic superstring
• Z_2\times Z_2$ orbifold compactification as the origin of realistic free fermionic models
• Chiral family classification of fermionic Z2xZ2 heterotic orbifold models
• Classification of the chiral Z2XZ2 fermionic models in the heterotic superstring
• String Duality and Non-supersymmetric Strings
• On orbifolds and free fermion constructions
• Stable Superstring Relics
• Spinor-Vector Duality in fermionic Z2XZ2 heterotic orbifold models
• Proton stability in superstring derived models
• Exophobic Quasi-Realistic Heterotic String Vacua
• Classification of Heterotic Pati-Salam Models
• Chiral Heterotic Strings with Positive Cosmological Constant
• Stable Superstring Relics and Ultrahigh Energy Cosmic Rays
• Genetic Algorithms and the Search for Viable String Vacua
• Z_2 x Z_2 Heterotic Orbifold Models of Non Factorisable Six Dimensional Toroidal Manifolds
• Bose-Fermi Degeneracy and Duality in Non-Supersymmetric Strings
• Doublet-Triplet Splitting in Realistic Heterotic String Derived models
• Non-Tachyonic Semi-Realistic Non-Supersymmetric Heterotic String Vacua
• Top Quark Mass in Exophobic Pati--Salam Heterotic String Model
• Classification of Standard-like Heterotic-String Vacua
• Toward the classification of the realistic free fermionic models
• Classification of Flipped SU(5) Heterotic-String Vacua
• Search for Free Fractional Electric Charge Elementary Particles
• T-duality orbifolds of heterotic Narain compactifications
• Moduli Fixing in Realistic String Vacua
• Towards the Classification of Tachyon-Free Models From Tachyonic Ten-Dimensional Heterotic String Vacua
• Heterotic free fermionic and symmetric toroidal orbifold models
• Moduli and Kähler potential in fermionic strings
• Classification of Left-Right Symmetric Heterotic String Vacua
• Top quark mass coupling and classification of weakly-coupled heterotic superstring vacua
• Type $\bar{0}$ Heterotic String Orbifolds
• Satisfiability Modulo Theories and Chiral Heterotic String Vacua with Positive Cosmological Constant
• Type 0 ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ Heterotic String Orbifolds and Misaligned Supersymmetry
• Vacuum Energy in Non-Supersymmetric Quasi-Realistic Heterotic-String Vacua with Fixed Moduli
• Towards Classification of $\mathcal{N}=1$ and $\mathcal{N}=0$ Flipped $SU(5)$ Asymmetric ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ Heterotic String Orbifolds
• Untwisted Moduli and Internal Fermions in Free Fermionic Strings