Affine $\mathcal{W}$-algebras and Miura maps from 3d $\mathcal N=4$ non-Abelian quiver gauge theories
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| author | Coman, Ioana Shim, Myungbo Yamazaki, Masahito Zhou, Yehao |
| author_facet | Coman, Ioana Shim, Myungbo Yamazaki, Masahito Zhou, Yehao |
| contents | We study Vertex Operator Algebras (VOAs) obtained from the H-twist of 3d $\mathcal{N}=4$ linear quiver gauge theories. We find that H-twisted VOAs can be regarded as the ''chiralization'' of the extended Higgs branch: many of the ingredients of the Higgs branch are naturally ''uplifted'' into the VOAs, while conversely the Higgs branch can be recovered as the associated variety of the VOA. We also discuss the connection of our VOA with affine $\mathcal{W}$-algebras. For example, we construct an explicit homomorphism from an affine $\mathcal{W}$-algebra $\mathcal{W}^{-n+1}(\mathfrak{gl}_n,f_{\mathrm{min}})$ into the H-twisted VOA for $T^{[2,1^{n-2}]}_{[1^n]}[\mathrm{SU}(n)]$ theories. Motivated by the relation with affine $\mathcal{W}$-algebras, we introduce a reduction procedure for the quiver diagram, and use this to give an algorithm to systematically construct novel free-field realizations for VOAs associated with general linear quivers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_13363 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Affine $\mathcal{W}$-algebras and Miura maps from 3d $\mathcal N=4$ non-Abelian quiver gauge theories Coman, Ioana Shim, Myungbo Yamazaki, Masahito Zhou, Yehao High Energy Physics - Theory Mathematical Physics Algebraic Geometry Quantum Algebra Representation Theory We study Vertex Operator Algebras (VOAs) obtained from the H-twist of 3d $\mathcal{N}=4$ linear quiver gauge theories. We find that H-twisted VOAs can be regarded as the ''chiralization'' of the extended Higgs branch: many of the ingredients of the Higgs branch are naturally ''uplifted'' into the VOAs, while conversely the Higgs branch can be recovered as the associated variety of the VOA. We also discuss the connection of our VOA with affine $\mathcal{W}$-algebras. For example, we construct an explicit homomorphism from an affine $\mathcal{W}$-algebra $\mathcal{W}^{-n+1}(\mathfrak{gl}_n,f_{\mathrm{min}})$ into the H-twisted VOA for $T^{[2,1^{n-2}]}_{[1^n]}[\mathrm{SU}(n)]$ theories. Motivated by the relation with affine $\mathcal{W}$-algebras, we introduce a reduction procedure for the quiver diagram, and use this to give an algorithm to systematically construct novel free-field realizations for VOAs associated with general linear quivers. |
| title | Affine $\mathcal{W}$-algebras and Miura maps from 3d $\mathcal N=4$ non-Abelian quiver gauge theories |
| topic | High Energy Physics - Theory Mathematical Physics Algebraic Geometry Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2312.13363 |