Non-abelian orbifolds of lattice vertex operator algebras

Thomas Gemünden; Christoph A. Keller

doi:10.1016/j.jalgebra.2021.06.023

Non-abelian orbifolds of lattice vertex operator algebras

Research output: Contribution to journal › Article › peer-review

Abstract

We construct orbifolds of holomorphic lattice vertex operator algebras for non-abelian finite automorphism groups G. To this end, we construct twisted modules for automorphisms g together with the projective representation of the centralizer of g on the twisted module. This allows us to extract the irreducible modules of the fixed-point VOA V^G, and to compute their characters and modular transformation properties. We then construct holomorphic VOAs by adjoining such modules to V^G. Applying these methods to extremal lattices in d=48 and d=72, we construct more than fifty new holomorphic VOAs of central charge 48 and 72, many of which have a very small number of light states.

Original language	English (US)
Pages (from-to)	656-696
Number of pages	41
Journal	Journal of Algebra
Volume	585
DOIs	https://doi.org/10.1016/j.jalgebra.2021.06.023
State	Published - Nov 1 2021
Externally published	Yes

Keywords

Conformal field theory
Conformal packing
Orbifold theory
Vertex operator algebras

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2021.06.023

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title = "Non-abelian orbifolds of lattice vertex operator algebras",

abstract = "We construct orbifolds of holomorphic lattice vertex operator algebras for non-abelian finite automorphism groups G. To this end, we construct twisted modules for automorphisms g together with the projective representation of the centralizer of g on the twisted module. This allows us to extract the irreducible modules of the fixed-point VOA VG, and to compute their characters and modular transformation properties. We then construct holomorphic VOAs by adjoining such modules to VG. Applying these methods to extremal lattices in d=48 and d=72, we construct more than fifty new holomorphic VOAs of central charge 48 and 72, many of which have a very small number of light states.",

keywords = "Conformal field theory, Conformal packing, Orbifold theory, Vertex operator algebras",

author = "Thomas Gem{\"u}nden and Keller, {Christoph A.}",

note = "Funding Information: Acknowledgments: We thank Terry Gannon, Klaus Lux, Sven M{\"o}ller and Nils Scheithauer for useful discussions. We thank Gerald H{\"o}hn and Yi-Zhi Huang for helpful discussions and comments on the draft. TG thanks the Department of Mathematics at University of Arizona for hospitality. We thank two anonymous referees for helpful comments on the draft. The work of TG is supported by the Swiss National Science Foundation Project Grant 175494 . Publisher Copyright: {\textcopyright} 2021 The Authors",

year = "2021",

month = nov,

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doi = "10.1016/j.jalgebra.2021.06.023",

language = "English (US)",

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pages = "656--696",

journal = "Journal of Algebra",

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T1 - Non-abelian orbifolds of lattice vertex operator algebras

AU - Gemünden, Thomas

AU - Keller, Christoph A.

N1 - Funding Information: Acknowledgments: We thank Terry Gannon, Klaus Lux, Sven Möller and Nils Scheithauer for useful discussions. We thank Gerald Höhn and Yi-Zhi Huang for helpful discussions and comments on the draft. TG thanks the Department of Mathematics at University of Arizona for hospitality. We thank two anonymous referees for helpful comments on the draft. The work of TG is supported by the Swiss National Science Foundation Project Grant 175494 . Publisher Copyright: © 2021 The Authors

PY - 2021/11/1

Y1 - 2021/11/1

N2 - We construct orbifolds of holomorphic lattice vertex operator algebras for non-abelian finite automorphism groups G. To this end, we construct twisted modules for automorphisms g together with the projective representation of the centralizer of g on the twisted module. This allows us to extract the irreducible modules of the fixed-point VOA VG, and to compute their characters and modular transformation properties. We then construct holomorphic VOAs by adjoining such modules to VG. Applying these methods to extremal lattices in d=48 and d=72, we construct more than fifty new holomorphic VOAs of central charge 48 and 72, many of which have a very small number of light states.

AB - We construct orbifolds of holomorphic lattice vertex operator algebras for non-abelian finite automorphism groups G. To this end, we construct twisted modules for automorphisms g together with the projective representation of the centralizer of g on the twisted module. This allows us to extract the irreducible modules of the fixed-point VOA VG, and to compute their characters and modular transformation properties. We then construct holomorphic VOAs by adjoining such modules to VG. Applying these methods to extremal lattices in d=48 and d=72, we construct more than fifty new holomorphic VOAs of central charge 48 and 72, many of which have a very small number of light states.

KW - Conformal field theory

KW - Conformal packing

KW - Orbifold theory

KW - Vertex operator algebras

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DO - 10.1016/j.jalgebra.2021.06.023

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EP - 696

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -

Non-abelian orbifolds of lattice vertex operator algebras

Abstract

Keywords

ASJC Scopus subject areas

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