TY - JOUR

T1 - Superconformal minimal models and admissible Jack polynomials

AU - Blondeau-Fournier, Olivier

AU - Mathieu, Pierre

AU - Ridout, David

AU - Wood, Simon

N1 - Publisher Copyright:
© 2017

PY - 2017/7/9

Y1 - 2017/7/9

N2 - 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.

AB - 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.

KW - Jack symmetric functions

KW - N=1 superconformal algebra

KW - Vertex operator super algebra

KW - Zhu algebra

UR - http://www.scopus.com/inward/record.url?scp=85019017010&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2017.04.026

DO - 10.1016/j.aim.2017.04.026

M3 - Article

SN - 0001-8708

VL - 314

SP - 71

EP - 123

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -