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Superconformal minimal models and admissible Jack polynomials

Blondeau-Fournier, O; Mathieu, Pierre; Ridout, David; Wood, Simon

Description

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,...[Show more]

dc.contributor.authorBlondeau-Fournier, O
dc.contributor.authorMathieu, Pierre
dc.contributor.authorRidout, David
dc.contributor.authorWood, Simon
dc.date.accessioned2020-12-20T20:57:56Z
dc.date.available2020-12-20T20:57:56Z
dc.identifier.issn0001-8708
dc.identifier.urihttp://hdl.handle.net/1885/218430
dc.description.abstractWe 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
dc.format.mimetypeapplication/pdf
dc.language.isoen_AU
dc.publisherAcademic Press
dc.sourceAdvances in Mathematics
dc.titleSuperconformal minimal models and admissible Jack polynomials
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume314
dc.date.issued2017
local.identifier.absfor010501 - Algebraic Structures in Mathematical Physics
local.identifier.ariespublicationa383154xPUB6998
local.type.statusPublished Version
local.contributor.affiliationBlondeau-Fournier, O, King’s College London
local.contributor.affiliationMathieu, Pierre, Université Laval
local.contributor.affiliationRidout, David, College of Science, ANU
local.contributor.affiliationWood, Simon, College of Science, ANU
local.bibliographicCitation.startpage71
local.bibliographicCitation.lastpage123
local.identifier.doi10.1016/j.aim.2017.04.026
dc.date.updated2020-11-23T11:11:45Z
local.identifier.scopusID2-s2.0-85019017010
local.identifier.thomsonID000403741500003
CollectionsANU Research Publications

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