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- W2963624521 abstract "Let V be the even part of the vertex operator super-algebra of r pairs of symplectic fermions. Up to two conjectures, we show that V admits a unique holomorphic extension if r is a multiple of 8, and no holomorphic extension otherwise. This is implied by two results obtained in this paper: (1) If r is a multiple of 8, one possible holomorphic extension is given by the lattice vertex operator algebra for the even self dual lattice $$D_{r}^+$$ with shifted stress tensor. (2) We classify Lagrangian algebras in $$mathcal {S}mathcal {F}(mathfrak {h})$$ , a ribbon category associated to symplectic fermions. The classification of holomorphic extensions of V follows from (1) and (2) if one assumes that $$mathcal {S}mathcal {F}(mathfrak {h})$$ is ribbon equivalent to $${mathrm {Rep}}(V)$$ , and that simple modules of extensions of V are in one-to-one relation with simple local modules of the corresponding commutative algebra in $$mathcal {S}mathcal {F}(mathfrak {h})$$ ." @default.
- W2963624521 created "2019-07-30" @default.
- W2963624521 creator A5022071312 @default.
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- W2963624521 date "2016-09-08" @default.
- W2963624521 modified "2023-09-26" @default.
- W2963624521 title "Holomorphic symplectic fermions" @default.
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- W2963624521 doi "https://doi.org/10.1007/s00209-016-1734-6" @default.
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