W-algebras of the Deligne-Cvitanović Exceptional series and the minimal 3d ${\mathcal N}=4$ SCFT
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915871597789184 |
|---|---|
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_17394 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| 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 |