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

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

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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 Wooden Frame With LED 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 Bottle shape opener the RG-flow of Argyres-Douglas theories as discussed by Buican and Nishinaka.