Journal article

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

David Ridout, Simon Wood

NUCLEAR PHYSICS B | ELSEVIER SCIENCE BV | Published : 2015

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..

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University of Melbourne Researchers

Grants

Awarded by Australian Research Council


Funding Acknowledgements

We thank Jim Borger for help with a question of commutative algebra, Jurgen Fuchs, Masoud Kamgarpour and Christoph Schweigert for illuminating discussions regarding parabolic Verma modules, Antun Milas for correspondence concerning the current status of higher rank generalisations, Ole Warnaar for advice on symmetric function theory, and the organisers of the Erwin Schrodinger Institute programme "Modern trends in topological quantum field theory" for their hospitality. DR's research is supported by the Australian Research Council Discovery Project DP1093910. SW's work is supported by the Australian Research Council Discovery Early Career Researcher Award DE140101825.