Abstract
We investigate the large N limit of permutation orbifolds of vertex operator algebras. To this end, we introduce the notion of nested oligomorphic permutation orbifolds and discuss under which conditions their fixed point VOAs converge. We show that if this limit exists, then it has the structure of a vertex algebra. Finally, we give an example based on mathrm {GL}(N,q) for which the fixed point VOA limit is also the limit of the full permutation orbifold VOA.
Highlights
Vertex Operator Algebras (VOA) and their conformal field theories (CFT) play an important in the AdS/CFT correspondence [1,20]
For the purposes of the AdS/CFT correspondence, physicists are most interested in the ‘large central charge limit,’ that is the limit of this family for N → ∞
Let us briefly discuss an example of a large N limit of a family of VOAs
Summary
Vertex Operator Algebras (VOA) and their conformal field theories (CFT) play an important in the AdS/CFT correspondence [1,20]. We build on previous work [4,5,13,19] to define and investigate such limits for permutation orbifolds of vertex operator algebras. We can try to extend V GN to a holomorphic VOA V orb(GN ) by adjoining a suitable set of modules For permutation orbifolds, this is always possible if c is a multiple of 24 [11]. To obtain a different growth behavior, in particular, slower growth, orbifolds without twisted modules are needed; the G L(N , q) example given above is of this type. It still grows exponentially fast: we find log dim V(onr)b ∼ n2
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