Trialities of W-algebras
Creutzig T, Linshaw AR (2022)
Publication Type: Journal article
Publication year: 2022
Journal
Book Volume: 10
Pages Range: 69-194
Journal Issue: 1
DOI: 10.4310/CJM.2022.v10.n1.a2
Abstract
We prove the conjecture of Gaiotto and Rapčák that the Y-algebras YL,M,N [ψ] with one of the parameters L, M, N zero, are simple one-parameter quotients of the universal two-parameter W1+∞-algebra, and satisfy a symmetry known as triality. These Y-algebras are defined as the cosets of certain non-principal W-algebras and W-superalgebras by their affine vertex subalgebras, and triality is an isomorphism between three such algebras. Special cases of our result provide new and unified proofs of many theorems and open conjectures in the literature on W-algebras of type A. This includes (1) Feigin-Frenkel duality, (2) the coset realization of principal W-algebras due to Arakawa and us, (3) Feigin and Semikha-tov’s conjectured triality between subregular W-algebras, principal W-superalgebras, and affine vertex superalgebras, (4) the rationality of subregular W-algebras due to Arakawa and van Ekeren, and (5) the identification of Heisenberg cosets of subregular W-algebras with principal rational W-algebras that was conjectured in the physics literature over 25 years ago. Finally, we prove the conjectures of Procházka and Rapčák on the explicit truncation curves realizing the simple Y-algebras as W1+∞-quotients, and on their minimal strong generating types.
Involved external institutions
Canada (CA)
United States (USA) (US)How to cite
APA:
Creutzig, T., & Linshaw, A.R. (2022). Trialities of W-algebras. Cambridge Journal of Mathematics, 10(1), 69-194. https://doi.org/10.4310/CJM.2022.v10.n1.a2
MLA:
Creutzig, Thomas, and Andrew R. Linshaw. "Trialities of W-algebras." Cambridge Journal of Mathematics 10.1 (2022): 69-194.
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