Journal article

Modularity of logarithmic parafermion vertex algebras

Jean Auger, Thomas Creutzig, David Ridout

LETTERS IN MATHEMATICAL PHYSICS | SPRINGER | Published : 2018

Abstract

The parafermionic cosets Ck= Com (H, Lk(sl2)) are studied for negative admissible levels k, as are certain infinite-order simple current extensions Bk of Ck. Under the assumption that the tensor theory considerations of Huang, Lepowsky and Zhang apply to Ck, irreducible Ck- and Bk-modules are obtained from those of Lk(sl2). Assuming the validity of a certain Verlinde-type formula likewise gives the Grothendieck fusion rules of these irreducible modules. Notably, there are only finitely many irreducible Bk-modules. The irreducible Ck- and Bk-characters are computed and the latter are shown, when supplemented by pseudotraces, to carry a finite-dimensional representation of the modular group. T..

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University of Melbourne Researchers

Grants

Awarded by Fonds de Recherche Nature et Technologies de Quebec


Awarded by Natural Sciences and Engineering Research Council of Canada


Awarded by Australian Research Council


Awarded by Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers


Funding Acknowledgements

We thank Shashank Kanade and Andrew Linshaw for discussions relating to the results presented here. J. A. is supported by a Doctoral Research Scholarship from the Fonds de Recherche Nature et Technologies de Quebec (184131). T. C. is supported by the Natural Sciences and Engineering Research Council of Canada (RES0020460). DR's research is supported by the Australian Research Council Discovery Project DP160101520 and the Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers CE140100049.