Screening operators for W-algebras

Abstract

Let $\mathfrak{g}$ be a simple finite-dimensional Lie superalgebra with a non-degenerate supersymmetric even invariant bilinear form, $f$ a nilpotent element in the even part of $\mathfrak{g}$, $\Gamma$ a good grading of $\mathfrak{g}$ for $f$ and ${\mathcal{W}}^k(\mathfrak{g},f;\Gamma )$ the $\mathcal{W}$-algebra associated with $\mathfrak{g},f,k,\Gamma$ defined by the generalized Drinfeld-Sokolov reduction. In this paper, we present each $\mathcal{W}$-algebra as the intersection of kernels of the screening operators, acting on the tensor vertex superalgebra of an affine vertex superalgebra and a neutral free superfermion vertex superalgebra. As applications, we prove that the $\mathcal{W}$-algebra associated with a regular nilpotent element in $\mathfrak{osp}(1,2n)$ is isomorphic to the $\mathcal{W}{B}_n$-algebra introduced by Fateev and Lukyanov, and that the $\mathcal{W}$-algebra associated with a subregular nilpotent element in ${\mathfrak{sl}}_n$ is isomorphic to the ${\mathcal{W}}_n^{(2)}$-algebra introduced by Feigin and Semikhatov.

revised version, to appear in Sel. Math. New Ser

References in corpus (1)

• Unitary W-algebras and three-dimensional higher spin gravities with spin one symmetry

Cited by in corpus (21)

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• Schur-Weyl Duality for Heisenberg Cosets
• Duality of subregular W-algebras and principal W-superalgebras
• Orbifolds and cosets of minimal $\mathcal{W}$-algebras
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• Trialities of orthosymplectic $\mathcal{W}$-algebras
• Cosets of the ${\mathcal{W}}^k({\mathfrak{sl}}_4,f_{\text{subreg}})$-algebra
• Screening operators and Parabolic inductions for Affine W-algebras (with an appendix by Shigenori Nakatsuka)
• Correspondences among CFTs with different W-algebra symmetry
• Higher Airy structures, W algebras and topological recursion
• Coproduct for affine Yangians and parabolic induction for rectangular $W$-algebras
• Subregular W-algebras of type A
• Whittaker vectors for $\mathcal{W}$-algebras from topological recursion
• Cosets of free field algebras via arc spaces
• Affine $\mathcal{W}$-algebras and Miura maps from 3d $\mathcal{N}=4$ non-Abelian quiver gauge theories
• Strong generators of the subregular W-algebra and combinatorial description at critical level
• On Miura maps for W-superalgebras
• On the structure of W-algebras in type A
• On the representation theory of the vertex algebra $L_{-5/2}(sl(4))$
• Orthosymplectic Feigin-Semikhatov duality
• Duality via convolution of W-algebras