Logarithmic W-algebras and Argyres-Douglas theories at higher rank

Abstract

Families of vertex algebras associated to nilpotent elements of simply-laced Lie algebras are constructed. These algebras are close cousins of logarithmic W-algebras of Feigin and Tipunin and they are also obtained as modifications of semiclassical limits of vertex algebras appearing in the context of $S$-duality for four-dimensional gauge theories. In the case of type $A$ and principal nilpotent element the character agrees precisely with the Schur-Index formula for corresponding Argyres-Douglas theories with irregular singularities. For other nilpotent elements they are identified with Schur-indices of type IV Argyres-Douglas theories. Further, there is a conformal embedding pattern of these vertex operator algebras that nicely matches the RG-flow of Argyres-Douglas theories as discussed by Buican and Nishinaka.

Comments are welcome

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• On ribbon categories for singlet vertex algebras
• Tensor categories of affine Lie algebras beyond admissible levels
• Braided Tensor Categories related to ${\mathcal{B}}_p$ Vertex Algebras
• Rationalizing CFTs and Anyonic Imprints on Higgs Branches
• Schur sector of Argyres-Douglas theory and $W$-algebra
• On the Correspondence between Surface Operators in Argyres-Douglas Theories and Modules of Chiral Algebra
• Vanishing OPE Coefficients in 4d N=2 SCFTs
• Admissible-level ${\mathfrak{sl}}_3$ minimal models
• Closed form fermionic expressions for the Macdonald index
• Characterizing braided tensor categories associated to logarithmic vertex operator algebras
• Deformation quantizations from vertex operator algebras
• Arc spaces and chiral symplectic cores
• On the Feigin-Tipunin conjecture
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• Peculiar Index Relations, 2D TQFT, and Universality of SUSY Enhancement
• W algebra, Cosets and VOA for 4d N = 2 SCFT from M5 branes
• Free field realisation and the chiral universal centraliser
• Bridging 4D QFTs and 2D VOAs via 3D high-temperature EFTs
• 4d $\mathcal{N}=2$ SCFTs and lisse W-algebras
• Categories of Weight Modules for Unrolled Restricted Quantum Groups at Roots of Unity
• Associated varieties of simple affine VOAs $L_k(s{l}_3)$ and $W$-algebras $W_k(s{l}_3,f)$
• Vanishing short multiplets in rank one 4d/5d SCFTs
• Relaxed and logarithmic modules of $\widehat{{\mathfrak{sl}}_3}$