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Limits of Vertex Algebras and Large N Factorization

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Abstract

We investigate the limit of sequences of vertex algebras. We discuss under what condition the vector space direct limit of such a sequence is again a vertex algebra. We then apply this framework to permutation orbifolds of vertex operator algebras and their large N limit. We establish that for any nested oligomorphic permutation orbifold such a large N limit exists, and we give a necessary and sufficient condition for that limit to factorize. This helps clarify the question of what VOAs can give rise to holographic conformal field theories in physics.

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Acknowledgements

We thank Klaus Lux for useful discussions. TG thanks the Department of Mathematics at University of Arizona for hospitality. The work of TG was supported by the Swiss National Science Foundation Project Grant 175494. The work of CAK is supported in part by the Simons Foundation Grant No. 629215 and by NSF Grant 2111748.

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  1. Independent, Bayes House, London, UK

    Thomas Gemünden

  2. Department of Mathematics, University of Arizona, Tucson, AZ, 85721-0089, USA

    Christoph A. Keller

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  1. Thomas Gemünden
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  2. Christoph A. Keller
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Correspondence to Christoph A. Keller.

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The work of TG was supported by the Swiss National Science Foundation Project Grant 175494. The work of CAK is supported in part by the Simons Foundation Grant No. 629215 and by NSF Grant 2111748. The authors have no relevant financial or non-financial interests to disclose.

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Communicated by C. Schweigert.

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Gemünden, T., Keller, C.A. Limits of Vertex Algebras and Large N Factorization. Commun. Math. Phys. 401, 3123–3148 (2023). https://doi.org/10.1007/s00220-023-04712-x

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