Holomorphic symplectic fermions

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...

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Bibliographic Details
Published in:Mathematische Zeitschrift 2017-04, Vol.285 (3-4), p.967-1006
Main Authors: Davydov, Alexei, Runkel, Ingo
Format: Article
Language:English
Subjects:
Algebra
Fermions
Mathematical analysis
Mathematics
Mathematics and Statistics
Modules
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Summary: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 S F ( h ) , a ribbon category associated to symplectic fermions. The classification of holomorphic extensions of V follows from (1) and (2) if one assumes that S F ( h ) is ribbon equivalent to 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 S F ( h ) .
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-016-1734-6