Orthosymplectic Feigin-Semikhatov duality

2023/07/27 by Fasquel, Justine, Nakatsuka, Shigenori
#17B69 (Primary) 17B67 (Secondary) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2307.14574

Abstract

We study the representation theory of the subregular W-algebra W^k(\mathfrakso_2n+1,f_sub) of type B and the principal W-superalgebra W^ℓ(\mathfrakosp_2|2n), which are related by an orthosymplectic analogue of Feigin-Semikhatov duality in type A. We establish a block-wise equivalence of weight modules over the W-superalgebras by using the relative semi-infinite cohomology functor and spectral flow twists, which generalizes the result of Feigin-Semikhatov-Tipunin for the N=2 superconformal algebra. In particular, the correspondence of Wakimoto type free field representations is obtained. When the level of the subregular W-algebra is exceptional, we classify the simple modules over the simple quotients W_k(\mathfrakso_2n+1,f_sub) and W_ℓ(\mathfrakosp_2|2n) and derive the character formulae.

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