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- W4362707072 abstract "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 the 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-K{a}hler varieties. From this relation, it follows that the VOA associated with the 3d mirror of $N$-flavors $U(1)$ 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 OPEs of elements in the BRST cohomology and find a new algebra which is a fermionic extension of a Bershadsky-Polyakov algebra $W^{-2}(mathfrak{sl}_3, f_{text{sub}})$. We also suggest an expression of 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." @default.
- W4362707072 created "2023-04-09" @default.
- W4362707072 creator A5065071690 @default.
- W4362707072 date "2023-04-06" @default.
- W4362707072 modified "2023-09-27" @default.
- W4362707072 title "Fermionic extensions of $W$-algebras via 3d $mathcal{N}=4$ gauge theories with a boundary" @default.
- W4362707072 doi "https://doi.org/10.48550/arxiv.2304.03270" @default.
- W4362707072 hasPublicationYear "2023" @default.
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