Limits of Vertex Algebras and Large N Factorization

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.

arXiv comment18 pages

References in corpus (8)

• Large N Field Theories, String Theory and Gravity
• Elliptic Genera of Symmetric Products and Second Quantized Strings
• Correlation functions for M^N/S_N orbifolds
• Systematic approach to cyclic orbifolds
• Characters and modular properties of permutation orbifolds
• String Universality for Permutation Orbifolds
• Permutation orbifolds and holography
• Direct limit completions of vertex tensor categories

Cited by in corpus (3)

• Conformal field theories dual to quantum gravity with strongly coupled matter
• The Chiral Ring of a Symmetric Orbifold and its Large N Limit
• Searching for strongly coupled AdS matter with multi-trace deformations