W-algebras of the Deligne-Cvitanović Exceptional series and the minimal 3d ${\mathcal N}=4$ SCFT

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Autores principales: Creutzig, Thomas, Garner, Niklas, Go, Byeonggi, Kim, Heeyeon
Formato: Preprint
Publicado: 2026
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author Creutzig, Thomas
Garner, Niklas
Go, Byeonggi
Kim, Heeyeon
author_facet Creutzig, Thomas
Garner, Niklas
Go, Byeonggi
Kim, Heeyeon
contents We propose a three-dimensional field theory construction that realizes the vertex algebras associated with the intermediate Lie algebras and the related $C_2$-cofinite minimal $W$-algebras of the Deligne-Cvitanović (DC) series as boundary algebras. The construction is based on the minimal three-dimensional ${\mathcal N}=4$ superconformal field theory coupled to a topological field theory. For a Neumann-type boundary condition compatible with the topological $A$-twist, the algebra of boundary local operators realizes the minimal $W$-algebra $W_{-h^\vee/6}(\mathfrak{g},f_{\text{min}})$. While this boundary condition is not deformable to the $B$-twist, we argue that a holomorphic-topological ($HT^B$) twist instead realizes the level-one affine algebras of the intermediate Lie algebras, providing a uniform three-dimensional origin for these vertex algebra structures.
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id arxiv_https___arxiv_org_abs_2603_17394
institution arXiv
publishDate 2026
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spellingShingle W-algebras of the Deligne-Cvitanović Exceptional series and the minimal 3d ${\mathcal N}=4$ SCFT
Creutzig, Thomas
Garner, Niklas
Go, Byeonggi
Kim, Heeyeon
High Energy Physics - Theory
Quantum Algebra
Representation Theory
We propose a three-dimensional field theory construction that realizes the vertex algebras associated with the intermediate Lie algebras and the related $C_2$-cofinite minimal $W$-algebras of the Deligne-Cvitanović (DC) series as boundary algebras. The construction is based on the minimal three-dimensional ${\mathcal N}=4$ superconformal field theory coupled to a topological field theory. For a Neumann-type boundary condition compatible with the topological $A$-twist, the algebra of boundary local operators realizes the minimal $W$-algebra $W_{-h^\vee/6}(\mathfrak{g},f_{\text{min}})$. While this boundary condition is not deformable to the $B$-twist, we argue that a holomorphic-topological ($HT^B$) twist instead realizes the level-one affine algebras of the intermediate Lie algebras, providing a uniform three-dimensional origin for these vertex algebra structures.
title W-algebras of the Deligne-Cvitanović Exceptional series and the minimal 3d ${\mathcal N}=4$ SCFT
topic High Energy Physics - Theory
Quantum Algebra
Representation Theory
url https://arxiv.org/abs/2603.17394