Journal article
Representations of the Nappi–Witten vertex operator algebra
A Babichenko, K Kawasetsu, D Ridout, W Stewart
Letters in Mathematical Physics | Published : 2021
Abstract
The Nappi–Witten model is a Wess–Zumino–Witten model in which the target space is the nonreductive Heisenberg group H4. We consider the representation theory underlying this conformal field theory. Specifically, we study the category of weight modules, with finite-dimensional weight spaces, over the associated affine vertex operator algebra H4. In particular, we classify the irreducible H4-modules in this category and compute their characters. We moreover observe that this category is nonsemisimple, suggesting that the Nappi–Witten model is a logarithmic conformal field theory.
Grants
Awarded by Ministry of Education, Culture, Sports, Science and Technology
Funding Acknowledgements
We are thankful to Cuipo Jiang and Thomas Quella for interesting discussion related to this research. KK's research is partially supported by MEXT Japan "Leading Initiative for Excellent Young Researchers (LEADER)", JSPS Kakenhi Grant numbers 19KK0065 and 19J01093 andAustralian Research Council Discovery Project DP160101520. DR's research is supported by the Australian Research Council Discovery Project DP160101520 and the Australian Research Council Future Fellowship FT200100431. WS's research is supported by an Australian Government Research Training Program (RTP) Scholarship.