Admissible level osp(1|2) minimal models and their relaxed highest weight modules

Wood, Simon ORCID: https://orcid.org/0000-0002-8257-0378 2020. Admissible level osp(1|2) minimal models and their relaxed highest weight modules. Transformation Groups 25 , pp. 887-943. 10.1007/s00031-020-09567-3

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Abstract

The minimal model osp(1|2) vertex operator superalgebras are the simple quotients of affine vertex operator superalgebras constructed from the affine Lie super algebra osp(1|2) at certain rational values of the level k. We classify all isomorphism classes of Z2-graded simple relaxed highest weight modules over the minimal model osp(1|2) vertex operator superalgebras in both the Neveu-Schwarz and Ramond sectors. To this end, we combine free field realisations, screening operators and the theory of symmetric functions in the Jack basis to compute explicit presentations for the Zhu algebras in both the Neveu-Schwarz and Ramond sectors. Two different free field realisations are used depending on the level. For k < −1, the free field realisation resembles the Wakimoto free field realisation of affine sl(2) and is originally due to Bershadsky and Ooguri. It involves 1 free boson (or rank 1 Heisenberg vertex algebra), one βγ bosonic ghost system and one bc fermionic ghost system. For k > −1, the argument presented here requires the bosonisation of the βγ system by embedding it into an indefinite rank 2 lattice vertex algebra.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Springer Verlag
ISSN:	1083-4362
Date of First Compliant Deposit:	28 August 2019
Date of Acceptance:	6 June 2019
Last Modified:	03 May 2023 20:44
URI:	https://orca.cardiff.ac.uk/id/eprint/125098

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