Rational vertex operator algebras and the effective central charge

@article{Dong2002RationalVO,
  title={Rational vertex operator algebras and the effective central charge},
  author={Chongying Dong and Geoffrey Mason},
  journal={International Mathematics Research Notices},
  year={2002},
  volume={2004},
  pages={2989-3008}
}
  • C. Dong, G. Mason
  • Published 31 January 2002
  • Mathematics
  • International Mathematics Research Notices
We establish that the Lie algebra of weight 1 states in a (strongly) rational vertex operator algebra is reductive, and that its Lie rank 1 is bounded above by the effective central charge c~. We show that lattice vertex operator algebras may be characterized by the equalities c~=l=c, and in particular holomorphic lattice theories may be characterized among all holomorphic vertex operator algebras by the equality l = c. 

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References

SHOWING 1-10 OF 24 REFERENCES

Holomorphic vertex operator algebras of small central charge

We provide a rigorous mathematical foundation to the study of strongly rational, holomorphic vertex operator algebras V of central charge c = 8, 16 and 24 initiated by Schellekens. If c = 8 or 16 we

Twisted representations of vertex operator algebras

This paper gives an analogue of Ag(V) theory for a vertex operator superalgebra V and an automorphism g of finite order. The relation between the g-twisted V-modules and Ag(V)-modules is established.

Regularity of Rational Vertex Operator Algebras

Rational vertex operator algebras, which play a fundamental role in rational conformal field theory (see [BPZ] and [MS]), single out an important class of vertex operator algebras. Most vertex

Modular invariance of characters of vertex operator algebras

In contrast with the finite dimensional case, one of the distinguished features in the theory of infinite dimensional Lie algebras is the modular invariance of the characters of certain

Meromorphic c = 24 Conformal Field Theories

. Modular invariant conformal field theories with just one primary field and central charge c = 24 are considered. It has been shown previously that if the chiral algebra of such a theory contains

Vertex operator algebras associated to representations of affine and Virasoro Algebras

The first construction of the integrable highest-weight representations of affine Lie algebras or loop algebras by Kac i-K] was greatly inspired by the generalization of the Weyl denominator formula

Local systems of vertex operators, vertex superalgebras and modules

Modular-Invariance of Trace Functions¶in Orbifold Theory and Generalized Moonshine

Abstract: The goal of the present paper is to provide a mathematically rigorous foundation to certain aspects of the theory of rational orbifold models in conformal field theory, in other words the

Vertex algebras, Kac-Moody algebras, and the Monster.

  • R. Borcherds
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1986
TLDR
An integral form is constructed for the universal enveloping algebra of any Kac-Moody algebras that can be used to define Kac's groups over finite fields, some new irreducible integrable representations, and a sort of affinization of anyKac-moody algebra.

On the classification of simple vertex operator algebras

Inspired by a recent work of Frenkel-Zhu, we study a class of (pre-)vertex operator algebras (voa) associated to the self-dual Lie algebras. Based on a few elementary structural results we propose