Orbifold construction and Lorentzian construction of Leech lattice vertex operator algebra

Abstract

We generalize Conway-Sloane's constructions of the Leech lattice from Niemeier lattices using Lorentzian lattice to holomorphic vertex operator algebras (VOA) of central charge 24. It provides a tool for analyzing the structures and relations among holomorphic VOAs related by orbifold construction. In particular, we are able to get some useful information about certain lattice subVOAs associated with the Cartan subalgebra of the weight one Lie algebra. We also obtain a relatively elementary proof that any strongly regular holomorphic VOA of central charge $24$ with a non-trivial weight one subspace can be constructed directly by a single orbifold construction from the Leech lattice VOA without using a dimension formula.

arXiv commentMinor changes; A mistake in Sec. 6.1.5 is fixed; to appear in J. Algebra

References in corpus (8)

• Modular invariance of trace functions in orbifold theory
• Meromorphic c=24 Conformal Field Theories
• Simple currents and extensions of vertex operator algebras
• C_2-cofiniteness of cyclic-orbifold models
• Construction and Classification of Holomorphic Vertex Operator Algebras
• Schellekens' List and the Very Strange Formula
• Dimension Formulae and Generalised Deep Holes of the Leech Lattice Vertex Operator Algebra
• Genus of vertex algebras and mass formula

Cited by in corpus (2)

• BPS Algebras in 2D String Theory
• Automorphism groups of cyclic orbifold vertex operator algebras associated with the Leech lattice and some non-prime isometries