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arXiv · 2209.14352

Limits of Vertex Algebras and Large N Factorization

Thomas Gemünden·Christoph A. Keller
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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 are candidates for holographic conformal field theories in physics.

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Thomas Gemünden, Christoph A. Keller. 2022-09-28. Limits of Vertex Algebras and Large N Factorization. https://doi.org/10.1007/s00220-023-04712-x

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