Fermionic extensions of $W$-algebras via 3d $\mathcal{N}=4$ gauge theories with a boundary
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911574665461760 |
|---|---|
| author | Yoshida, Yutaka |
| author_facet | Yoshida, Yutaka |
| contents | We study properties of vertex (operator) algebras associated with 3d H-twisted $\mathcal{N}=4$ supersymmetric gauge theories with a boundary. The vertex operator algebras (VOAs) are defined by BRST cohomologies of currents with symplectic bosons, complex fermions, and bc-ghosts. We point out that VOAs for 3d $\mathcal{N}=4$ abelian gauge theories are fermionic extensions of VOAs associated with toric hyper-Kähler varieties. From this relation, it follows that the VOA associated with the 3d mirror of $N$-flavor $U(1)$ SQED is a fermionic extension of a $W$-algebra $W^{-N+1}(\mathfrak{sl}_N, f_{\text{sub}})$. For $N=3$, we explicitly compute the OPE of elements in the BRST cohomology and find a new algebra that is a fermionic extension of a Bershadsky-Polyakov algebra $W^{-2}(\mathfrak{sl}_3, f_{\text{sub}})$. We also suggest an expression for the vacuum character of the fermionic extension of $W^{-N+1}(\mathfrak{sl}_N, f_{\text{sub}})$ predicted by 3d $\mathcal{N}=4$ mirror symmetry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_03270 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fermionic extensions of $W$-algebras via 3d $\mathcal{N}=4$ gauge theories with a boundary Yoshida, Yutaka High Energy Physics - Theory Mathematical Physics Quantum Algebra Representation Theory We study properties of vertex (operator) algebras associated with 3d H-twisted $\mathcal{N}=4$ supersymmetric gauge theories with a boundary. The vertex operator algebras (VOAs) are defined by BRST cohomologies of currents with symplectic bosons, complex fermions, and bc-ghosts. We point out that VOAs for 3d $\mathcal{N}=4$ abelian gauge theories are fermionic extensions of VOAs associated with toric hyper-Kähler varieties. From this relation, it follows that the VOA associated with the 3d mirror of $N$-flavor $U(1)$ SQED is a fermionic extension of a $W$-algebra $W^{-N+1}(\mathfrak{sl}_N, f_{\text{sub}})$. For $N=3$, we explicitly compute the OPE of elements in the BRST cohomology and find a new algebra that is a fermionic extension of a Bershadsky-Polyakov algebra $W^{-2}(\mathfrak{sl}_3, f_{\text{sub}})$. We also suggest an expression for the vacuum character of the fermionic extension of $W^{-N+1}(\mathfrak{sl}_N, f_{\text{sub}})$ predicted by 3d $\mathcal{N}=4$ mirror symmetry. |
| title | Fermionic extensions of $W$-algebras via 3d $\mathcal{N}=4$ gauge theories with a boundary |
| topic | High Energy Physics - Theory Mathematical Physics Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2304.03270 |