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Relaxed singular vectors, Jack symmetric functions and fractional level sl(2) models

Ridout, David and Wood, Simon 2015. Relaxed singular vectors, Jack symmetric functions and fractional level sl(2) models. Nuclear Physics B 894 , pp. 621-664. 10.1016/j.nuclphysb.2015.03.023

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Abstract

The fractional level models are (logarithmic) conformal field theories associated with affine Kac–Moody (super)algebras at certain levels k∈Q. They are particularly noteworthy because of several longstanding difficulties that have only recently been resolved. Here, Wakimoto's free field realisation is combined with the theory of Jack symmetric functions to analyse the fractional level sl(2) models. The first main results are explicit formulae for the singular vectors of minimal grade in relaxed Wakimoto modules. These are closely related to the minimal grade singular vectors in relaxed (parabolic) Verma modules. Further results include an explicit presentation of Zhu's algebra and an elegant new proof of the classification of simple relaxed highest weight modules over the corresponding vertex operator algebra. These results suggest that generalisations to higher rank fractional level models are now within reach.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: Elsevier
ISSN: 0550-3213
Date of First Compliant Deposit: 6 December 2016
Date of Acceptance: 18 March 2015
Last Modified: 04 Jun 2017 09:33
URI: http://orca.cf.ac.uk/id/eprint/96665

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