Rational Vertex Operator Algebras and the Effective Central Charge

Abstract

We establish that the Lie algebra of weight one states in a (strongly) rational vertex operator algebra is reductive, and that its Lie rank is bounded above by the effective central charge. We show that lattice vertex operator algebras may be characterized by the equalities of the effective central charge, the Lie rank and the central charge, and in particular holomorphic lattice theories may be characterized among all holomorphic vertex operator algebras by the equality of the Lie rank and the central charge.

latex 18 pages

References in corpus (3)

• Modular invariance of trace functions in orbifold theory
• Meromorphic c=24 Conformal Field Theories
• Holomorphic Vertex Operator Algebras of Small Central Charges

Cited by in corpus (9)

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• Dimension Formulae and Generalised Deep Holes of the Leech Lattice Vertex Operator Algebra
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• Systematic Orbifold Constructions of Schellekens' Vertex Operator Algebras from Niemeier Lattices
• Self-Dual Vertex Operator Superalgebras and Superconformal Field Theory
• Building vertex algebras from parts
• Cyclic orbifolds of lattice vertex operator algebras having group like fusions
• 51 constructions of the Moonshine module
• Genus of vertex algebras and mass formula