Quadratic spaces and holomorphic framed vertex operator algebras of central charge 24

Abstract

In 1993, Schellekens obtained a list of possible 71 Lie algebras of holomorphic vertex operator algebras with central charge 24. However, not all cases are known to exist. The aim of this article is to construct new holomorphic vertex operator algebras using the theory of framed vertex operator algebras and to determine the Lie algebra structures of their weight one subspaces. In particular, we study holomorphic framed vertex operator algebras associated to subcodes of the triply even codes $\RM(1,4)^3$ and $\RM(1,4)\oplus \EuD(d_{16}^+)$ of length 48. These vertex operator algebras correspond to the holomorphic simple current extensions of the lattice type vertex operator algebras $(V_{\sqrt{2}{E}_8}^{+}{)}^{\otimes 3}$ and $V_{\sqrt{2}{E}_8}^{+}\otimes V_{\sqrt{2}{D}_{16}^{+}}^{+}$. We determine such extensions using a quadratic space structure on the set of all irreducible modules $R(W)$ of $W$ when $W=(V_{\sqrt{2}{E}_8}^{+}{)}^{\otimes 3}$ or $V_{\sqrt{2}{E}_8}^{+}\otimes V_{\sqrt{2}{D}_{16}^{+}}^{+}$. As our main results, we construct seven new holomorphic vertex operator algebras of central charge 24 in Schellekens' list and obtain a complete list of all Lie algebra structures associated to the weight one subspaces of holomorphic framed vertex operator algebras of central charge 24.

46 pages

References in corpus (4)

• On triply even binary codes
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• The Automorphism Group of the Vertex Operator Algebra $V_L^{+}$ for an even lattice $L$ without roots
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Cited by in corpus (19)

• On triply even binary codes
• Dimension Formulae and Generalised Deep Holes of the Leech Lattice Vertex Operator Algebra
• Classification of Unitary RCFTs with Two Primaries and Central Charge Less Than 25
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• Orbifold construction of holomorphic vertex operator algebras associated to inner automorphisms
• Cyclic orbifolds of lattice vertex operator algebras having group like fusions
• A holomorphic vertex operator algebra of central charge $24$ whose weight one Lie algebra has type $A_{6,7}$
• Hecke Relations, Cosets and the Classification of 2d RCFTs
• Dimension Formulae in Genus Zero and Uniqueness of Vertex Operator Algebras
• A Holomorphic vertex operator algebra of central charge 24 with weight one Lie algebra $F_{4,6}{A}_{2,2}$
• Reverse orbifold construction and uniqueness of holomorphic vertex operator algebras
• Genus of vertex algebras and mass formula
• A characterization of vertex operator algebras $V_{Z\alpha }^{+}$: I
• On orbifold constructions associated with the Leech lattice vertex operator algebra
• Inertia groups and uniqueness of holomorphic vertex operator algebras
• Lattices, Vertex Algebras and Modular Categories
• Construction of holomorphic local conformal framed nets
• Application of a ${\mathbb{Z}}_3$-orbifold construction to the lattice vertex operator algebras associated to Niemeier lattices
• Mirror Extensions of Vertex Operator Algebras