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arXiv · 1809.01725

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

Thomas Creutzig
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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 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.

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Thomas Creutzig. 2018-09-05. Logarithmic W-algebras and Argyres-Douglas theories at higher rank. https://doi.org/10.1007/jhep11(2018)188

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