4d $\mathcal{N}=2$ SCFTs and lisse W-algebras

Understand

We continue our studies of the correspondence between 4d $\mathcal{N}=2$ SCFTs and 2d W-algebras.

• The purpose of this paper is to study the relationship between 2d lisse W-algebras and their 4d SCFT partners.
• The lisse W-algebra is the W-algebra whose associated Zhu's $C_2$ algebra is finite dimensional.
• As the associated variety of Zhu's $C_2$ algebra is identified with the Higgs branch in the 4d/2d correspondence, the lisse condition is equivalent to the absence of the Higgs branch on the 4d side.