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Construction and classification of holomorphic vertex operator algebras

  • Jethro van Ekeren , Sven Möller ORCID logo and Nils R. Scheithauer

Abstract

We develop an orbifold theory for finite, cyclic groups acting on holomorphic vertex operator algebras. Then we show that Schellekens’ classification of V1-structures of meromorphic conformal field theories of central charge 24 is a theorem on vertex operator algebras. Finally, we use these results to construct some new holomorphic vertex operator algebras of central charge 24 as lattice orbifolds.

Funding statement: The first author was supported by a grant from the Alexander von Humboldt Foundation and later by CAPES-Brazil. The second author was partially supported by a scholarship of the Studienstiftung des deutschen Volkes. The second and third author both were supported by the DFG-project “Infinite-dimensional Lie algebras in string theory”.

Acknowledgements

We thank P. Bantay, S. Carnahan, T. Creutzig, G. Höhn, Y.-Z. Huang, V. Kac, C.-H. Lam, M. Miyamoto, A. Schellekens, H. Shimakura and H. Yamauchi for valuable discussions and the referee for suggesting several improvements.

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Received: 2016-07-14
Revised: 2017-10-09
Published Online: 2017-11-16
Published in Print: 2020-02-01

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