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Superconformal minimal models and admissible Jack polynomials

Blondeau-Fournier, Olivier, Mathieu, Pierre, Ridout, David and Wood, Simon ORCID: 2017. Superconformal minimal models and admissible Jack polynomials. Advances in Mathematics 314 , pp. 71-123. 10.1016/j.aim.2017.04.026

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We give new proofs of the rationality of the N=1 superconformal minimal model vertex operator superalgebras and of the classification of their modules in both the Neveu–Schwarz and Ramond sectors. For this, we combine the standard free field realisation with the theory of Jack symmetric functions. A key role is played by Jack symmetric polynomials with a certain negative parameter that are labelled by admissible partitions. These polynomials are shown to describe free fermion correlators, suitably dressed by a symmetrising factor. The classification proofs concentrate on explicitly identifying Zhu's algebra and its twisted analogue. Interestingly, these identifications do not use an explicit expression for the non-trivial vacuum singular vector. While the latter is known to be expressible in terms of an Uglov symmetric polynomial or a linear combination of Jack superpolynomials, it turns out that standard Jack polynomials (and functions) suffice to prove the classification.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Uncontrolled Keywords: N=1 superconformal algebra; Zhu algebra; Jack symmetric functions; Vertex operator super algebra
Publisher: Elsevier
ISSN: 0001-8708
Funders: Australian Research Council
Date of Acceptance: 27 April 2017
Last Modified: 21 Oct 2022 07:43

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