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• W3130591347 abstract "Trialities of $mathcal{W}$-algebras are certain nontrivial isomorphisms between the affine cosets of three different $mathcal{W}$-(super)algebras, and were first conjectured in the physics literature by Gaiotto and Rapcak. In this paper we prove trialities among eight families of $mathcal{W}$-(super)algebras of types $B$, $C$, and $D$. The key idea is to identify the affine cosets of these algebras with one-parameter quotients of the universal two-parameter even spin $mathcal{W}_{infty}$-algebra which was recently constructed by Kanade and the second author. Our result is a vast generalization of both Feigin-Frenkel duality in types $B$, $C$, and $D$, and the coset realization of principal $mathcal{W}$-algebras of type $D$ due to Arakawa and us. It also provides a new coset realization of principal $mathcal{W}$-algebras of types $B$ and $C$. As an application, we prove the rationality of the affine vertex superalgebra $L_k(mathfrak{osp}_{1|2n})$, the minimal $mathcal{W}$-algebra $mathcal{W}_{k-1/2}(mathfrak{sp}_{2n+2}, f_{text{min}})$, and the coset $text{Com}(L_k(mathfrak{sp}_{2m}), L_k(mathfrak{sp}_{2n}))$, for all integers $k,n,m geq 1$ with $m<n$. We also prove the rationality of some families of principal $mathcal{W}$-superalgebras of $mathfrak{osp}_{1|2n}$ and $mathfrak{osp}_{2|2n}$, and subregular $mathcal{W}$-algebras of $mathfrak{so}_{2n+1}$" @default.
• W3130591347 created "2021-03-01" @default.
• W3130591347 creator A5036350064 @default.
• W3130591347 creator A5089933457 @default.
• W3130591347 date "2021-02-20" @default.
• W3130591347 modified "2023-09-27" @default.
• W3130591347 title "Trialities of orthosymplectic $mathcal{W}$-algebras" @default.
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• W3130591347 hasPublicationYear "2021" @default.
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