# 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} }

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.

## 14 Citations

71 holomorphic vertex operator algebras of central charge 24

- MathematicsBulletin of the Institute of Mathematics Academia Sinica NEW SERIES
- 2019

In this article, we give a survey on the recent progress towards the classification of strongly regular holomorphic vertex operator algebras of central charge 24. In particular, we review the…

Holomorphic vertex operator algebras of small central charge

- Mathematics
- 2002

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…

Automorphism groups and uniqueness of holomorphic vertex operator algebras of central charge $24$

- Mathematics
- 2022

. We describe the automorphism groups of all holomorphic vertex operator algebras of central charge 24 with non-trivial weight one Lie algebras by using their constructions as simple current…

Classification of holomorphic framed vertex operator algebras of central charge 24

- Mathematics
- 2012

This article is a continuation of our work on the classification of holomorphic framed vertex operator algebras of central charge 24. We show that a holomorphic framed VOA of central charge 24 is…

Shifted vertex operator algebras

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 2006

We study the properties of shifted vertex operator algebras, which are vertex algebras derived from a given theory by shifting the conformal vector. In this way, we are able to exhibit large numbers…

A holomorphic vertex operator algebra of central charge 24 whose weight one Lie algebra has type $${A_{6,7}}$$A6,7

- Mathematics
- 2016

In this article, we describe a construction of a holomorphic vertex operator algebras of central charge 24 whose weight one Lie algebra has type $${A_{6,7}}$$A6,7.

Representations of vertex operator algebras

- Mathematics
- 2006

This paper is an exposition of the representation theory of vertex operator algebras in terms of associative algebras A_n(V) and their bimodules. A new result on the rationality is given. That is, a…

Simple current extensions of vertex operator algebras by unitary modules

- Mathematics
- 2017

In this paper, a condition making vertex operator superalgebras to be unitary is determined and an analogue of conformal spin-statistics theorem in conformal field theory is proved. As an application…