Journal article

An admissible level (osp)over-cap (1 vertical bar 2)-model: modular transformations and the Verlinde formula

John Snadden, David Ridout, Simon Wood

LETTERS IN MATHEMATICAL PHYSICS | SPRINGER | Published : 2018

Abstract

The modular properties of the simple vertex operator superalgebra associated with the affine Kac–Moody superalgebra osp^ (1 | 2) at level -54 are investigated. After classifying the relaxed highest-weight modules over this vertex operator superalgebra, the characters and supercharacters of the simple weight modules are computed and their modular transforms are determined. This leads to a complete list of the Grothendieck fusion rules by way of a continuous superalgebraic analog of the Verlinde formula. All Grothendieck fusion coefficients are observed to be non-negative integers. These results indicate that the extension to general admissible levels will follow using the same methodology onc..

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University of Melbourne Researchers

Grants

Awarded by Australian Research Council Discovery Projects


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


Awarded by Australian Research Council Discovery Early Career Researcher Award


Awarded by Australian Research Council Discovery Project


Funding Acknowledgements

DR thanks Kenji Iohara for illuminating discussions on the structure of Verma modules over osp(1|2). We would like to thank the anonymous referee whose careful reading of the original manuscript and many suggestions significantly improved the article. JS's research is supported by a University Research Scholarship from the Australian National University. DR's research is supported by the Australian Research Council Discovery Projects DP1093910 and DP160101520 as well as the Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers CE140100049. SW's research is supported by Australian Research Council Discovery Early Career Researcher Award DE140101825 and the Australian Research Council Discovery Project DP160101520.