The universal N=2 supersymmetric W_infty algebra exists as a 2-parameter family whose Y-algebra quotients satisfy the conjectured dualities, giving coset realizations and strong rationality for W_k(sl_{n+1|n}) at k = -1 + 1/(n+a+1).
Chiral algebras of class $\mathcal{S}$ and Moore-Tachikawa symplectic varieties
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abstract
We give a functorial construction of the genus zero chiral algebras of class $\mathcal{S}$, that is, the vertex algebras corresponding to the theory of class $\mathcal{S}$ associated with genus zero pointed Riemann surfaces via the 4d/2d duality discovered by Beem, Lemos, Liendo, Peelaers, Rastelli and van Rees in physics. We show that there is a unique family of vertex algebras satisfying the required conditions and show that they are all simple and conformal. In fact, our construction works for any complex semisimple group G that is not necessarily simply laced. Furthermore, we show that the associated varieties of these vertex algebras are exactly the genus zero Moore-Tachikawa symplectic varieties that have been recently constructed by Braverman, Finkelberg and Nakajima using the geometry of the affine Grassmannian for the Langlands dual group.
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UNVERDICTED 5representative citing papers
An operadic order-by-order deformation-obstruction theory for chiral quantizations of vertex Poisson algebras, controlled by chiral Poisson cohomology, with reduction to de Rham cohomology for affine symplectic varieties and rigidity for Virasoro minimal models.
For m=1 the algebra L_{k1}(D4) is quasi-lisse with associated variety the Zariski closure of the subregular nilpotent orbit and possesses a unique irreducible ordinary module.
Proves holonomicity of conformal blocks sheaves and that flat sections are spanned by trace functions for quasi-lisse vertex algebras satisfying finiteness and semisimplicity, generalizing Zhu's theorem with a dimension coincidence for admissible affine cases.
Introduces cohomology rings, Hodge numbers and Witten index for unitary N=(2,2) full VOAs; constructs spectral flow algebraically and proves its periodicities equivalent to top-degree cohomology classes, yielding Poincaré duality, T-duality and Frobenius structures.
citing papers explorer
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Universal $2$-parameter $\mathcal{N}=2$ supersymmetric $\mathcal{W}_{\infty}$-algebra
The universal N=2 supersymmetric W_infty algebra exists as a 2-parameter family whose Y-algebra quotients satisfy the conjectured dualities, giving coset realizations and strong rationality for W_k(sl_{n+1|n}) at k = -1 + 1/(n+a+1).
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On the deformation theory of chiral quantizations
An operadic order-by-order deformation-obstruction theory for chiral quantizations of vertex Poisson algebras, controlled by chiral Poisson cohomology, with reduction to de Rham cohomology for affine symplectic varieties and rigidity for Virasoro minimal models.
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A new quasi-lisse affine vertex algebra of type $D_4$
For m=1 the algebra L_{k1}(D4) is quasi-lisse with associated variety the Zariski closure of the subregular nilpotent orbit and possesses a unique irreducible ordinary module.
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Modular invariance of characters of quasi-lisse vertex algebras
Proves holonomicity of conformal blocks sheaves and that flat sections are spanned by trace functions for quasi-lisse vertex algebras satisfying finiteness and semisimplicity, generalizing Zhu's theorem with a dimension coincidence for admissible affine cases.
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Cohomology ring of unitary $N=(2,2)$ full vertex algebra and mirror symmetry
Introduces cohomology rings, Hodge numbers and Witten index for unitary N=(2,2) full VOAs; constructs spectral flow algebraically and proves its periodicities equivalent to top-degree cohomology classes, yielding Poincaré duality, T-duality and Frobenius structures.