Correspondences of Categories for Subregular W -Algebras and Principal W -Superalgebras

Creutzig T, Genra N, Nakatsuka S, Sato R (2022)

Publication Type: Journal article

Publication year: 2022

Journal

Communications in Mathematical Physics Springer Verlag (Germany)

Book Volume: 393

Pages Range: 1-60

Journal Issue: 1

DOI: 10.1007/s00220-021-04297-3

Abstract

Based on the Kazama–Suzuki type coset construction and its inverse coset between the subregular W-algebras for sln and the principal W-superalgebras for sl1|n, we prove weight-wise linear equivalences of their representation categories. Our main results are then improvements of these correspondences incorporating the monoidal structures. Firstly, in the rational case, we obtain the classification of simple modules and their fusion rules via simple current extensions from their Heisenberg cosets. Secondly, beyond the rational case, we use certain kernel VOAs together with relative semi-infinite cohomology functors to get functors from categories of modules for the subregular W-algebras for sln to categories of modules for the principal W-superalgebras for sl1|n and vice versa. We study these functors and in particular prove isomorphisms between the superspaces of logarithmic intertwining operators. As a corollary, we obtain correspondences of representation categories in the monoidal sense beyond the rational case as well.

Involved external institutions

University of Alberta CA Canada (CA) University of Tokyo JP Japan (JP)

How to cite

APA:

Creutzig, T., Genra, N., Nakatsuka, S., & Sato, R. (2022). Correspondences of Categories for Subregular W -Algebras and Principal W -Superalgebras. Communications in Mathematical Physics, 393(1), 1-60. https://doi.org/10.1007/s00220-021-04297-3

MLA:

Creutzig, Thomas, et al. "Correspondences of Categories for Subregular W -Algebras and Principal W -Superalgebras." Communications in Mathematical Physics 393.1 (2022): 1-60.

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