Abstract
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 C2 algebra is finite dimensional. As the associated variety of Zhu’s C2 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. We classify 4d \( \mathcal{N} \) = 2 SCFTs which do not admit Higgs branch, then these theories would give lisse W-algebras through the 4d/2d correspondence. In particular, we predict the existence of a large class of new non-admissible lisse W-algebras, which have not been studied before. The 4d theories corresponding to lisse W-algebra can appear in the Higgs branches of generic 4d \( \mathcal{N} \) = 2 SCFTs, therefore they are crucial to understand the Higgs branches of \( \mathcal{N} \) = 2 SCFTs.
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Xie, D., Yan, W. 4d \( \mathcal{N} \) = 2 SCFTs and lisse W-algebras. J. High Energ. Phys. 2021, 271 (2021). https://doi.org/10.1007/JHEP04(2021)271
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DOI: https://doi.org/10.1007/JHEP04(2021)271