Niemeier Lattices in the Free Fermionic Heterotic-String Formulation

Abstract

The spinor-vector duality was discovered in free fermionic constructions of the heterotic-string in four dimensions. It played a key role in the construction of heterotic-string models with an anomaly free extra $Z^{\prime }$ symmetry that may remain unbroken down to low energy scales. A generic signature of the low scale string derived $Z^{\prime }$ model is via di-photon excess that may be within reach of the LHC. A fascinating possibility is that the spinor-vector duality symmetry is rooted in the structure of the heterotic-string compactifications to two dimensions. The two dimensional heterotic-string theories are in turn related to the so-called moonshine symmetries that underlie the two dimensional compactifications. In this paper we embark on exploration of this connection by the free fermionic formulation to classify the symmetries of the two dimensional heterotic-string theories. We use two complementary approaches in our classification. The first utilises a construction which is akin to the one used in the spinor-vector duality. Underlying this method is the triality property of $SO(8)$ representations. In the second approach we use the free fermionic tools to classify the twenty four dimensional Niemeier lattices.

22 pages. Standard LaTex. 1 figure. Title changed in journal. Minor corrections. Published version

References in corpus (19)

• A Mini-Landscape of Exact MSSM Spectra in Heterotic Orbifolds
• Statistics on the Heterotic Landscape: Gauge Groups and Cosmological Constants of Four-Dimensional Heterotic Strings
• Chiral family classification of fermionic Z2xZ2 heterotic orbifold models
• Spinor-Vector Duality in fermionic Z2XZ2 heterotic orbifold models
• Classification of Heterotic Pati-Salam Models
• Spinor-Vector Duality in Heterotic SUSY Vacua
• Z_2 x Z_2 Heterotic Orbifold Models of Non Factorisable Six Dimensional Toroidal Manifolds
• Minimal Standard Heterotic String Models
• Spinor-Vector Duality in N=2 Heterotic String Vacua
• Classification of Flipped SU(5) Heterotic-String Vacua
• Interpreting the 750 GeV digamma excess: a review
• Orbifold Symmetry Reductions of Massive Boson-Fermion Degeneracy
• Spinor-Vector Duality in Heterotic String Orbifolds
• Massive Boson-Fermion Degeneracy and the Early Structure of the Universe
• A Light Z' Heterotic-String Derived Model
• Heterotic free fermionic and symmetric toroidal orbifold models
• Generalised Umbral Moonshine
• The LHC di-photon excess and Gauge Coupling Unification in Extra $Z^{\prime }$ Heterotic-String Derived Models
• Elementary introduction to Moonshine

Cited by in corpus (5)

• Classification of Standard-like Heterotic-String Vacua
• Towards the Classification of Tachyon-Free Models From Tachyonic Ten-Dimensional Heterotic String Vacua
• Classification of Left-Right Symmetric Heterotic String Vacua
• Spinor-Vector Duality and Mirror Symmetry
• Spinor-Vector Duality and the Swampland