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Holomorphic Symplectic Fermions | | Alexei Davydov
; Ingo Runkel
; | | Date: |
25 Jan 2016 | | 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 SF(h), a ribbon category
associated to symplectic fermions.
The classification of holomorphic extensions of V follows from 1) and 2) if
one assumes that SF(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 SF(h). | | Source: | arXiv, 1601.6451 | | Services: | Forum | Review | PDF | Favorites | |
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