A conjectured 4d mirror symmetry for A1 class-S theories matches simple modules of the Higgs-branch VOA to fixed manifolds of the Hitchin Coulomb branch, with conformal weights and modular Jordan types fixed by moment-map values and manifold dimensions.
Joseph ideals and lisse minimal W-algebras
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abstract
We consider a lifting of Joseph ideals for the minimal nilpotent orbit closure to the setting of affine Kac-Moody algebras and find new examples of affine vertex algebras whose associated varieties are minimal nilpotent orbit closures. As an application we obtain a new family of lisse ($C_2$-cofinite) W-algebras that are not coming from admissible representations of affine Kac-Moody algebras.
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Mirror symmetry for 4d $A_1$ class-$\mathcal{S}$ theories: modularity, defects and Coulomb branch
A conjectured 4d mirror symmetry for A1 class-S theories matches simple modules of the Higgs-branch VOA to fixed manifolds of the Hitchin Coulomb branch, with conformal weights and modular Jordan types fixed by moment-map values and manifold dimensions.