N = 4 Superconformal Algebras and Diagonal Cosets
Creutzig T, Feigin B, Linshaw AR (2022)
Publication Type: Journal article
Publication year: 2022
Journal
Book Volume: 2022
Pages Range: 2180-2223
Journal Issue: 3
DOI: 10.1093/imrn/rnaa078
Abstract
Coset constructions of W-algebras have many applications and were recently given for principal W-algebras of A, D, and E types by Arakawa together with the 1st and 3rd authors. In this paper, we give coset constructions of the large and small N = 4 superconformal algebras, which are the minimal W-algebras of d(2, 1; α) and psl(2|2), respectively. From these realizations, one finds a remarkable connection between the large N = 4 algebra and the diagonal coset Ck1,k2 = Com(Vk1+k2 (sl2),Vk1 (sl2) ⊗ Vk2 (sl2)), namely, as two-parameter vertex algebras, Ck1,k2 coincides with the coset of the large N = 4 algebra by its affine subalgebra. We also show that at special points in the parameter space, the simple quotients of these cosets are isomorphic to various Walgebras. As a corollary, we give new examples of strongly rational principalW-algebras of type C at degenerate admissible levels.
Authors with CRIS profile
Involved external institutions
University of Alberta
Canada (CA)
National Research University - Higher School of Economics (HSE) / Высшая школа экономики
Russian Federation (RU)
University of Denver
United States (USA) (US)
Canada (CA)
National Research University - Higher School of Economics (HSE) / Высшая школа экономики
Russian Federation (RU)
University of Denver
United States (USA) (US)
How to cite
APA:
Creutzig, T., Feigin, B., & Linshaw, A.R. (2022). N = 4 Superconformal Algebras and Diagonal Cosets. International Mathematics Research Notices, 2022(3), 2180-2223. https://doi.org/10.1093/imrn/rnaa078
MLA:
Creutzig, Thomas, Boris Feigin, and Andrew R. Linshaw. "N = 4 Superconformal Algebras and Diagonal Cosets." International Mathematics Research Notices 2022.3 (2022): 2180-2223.
BibTeX: Download