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

Abstract We continue our studies of the correspondence between 4d N $$ \mathcal{N} $$ = 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...

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Bibliographic Details
Main Authors: Dan Xie, Wenbin Yan
Format: Article
Language:English
Published: SpringerOpen 2021-04-01
Series:Journal of High Energy Physics
Subjects:
Online Access:https://doi.org/10.1007/JHEP04(2021)271
Description
Summary:Abstract We continue our studies of the correspondence between 4d N $$ \mathcal{N} $$ = 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. We classify 4d N $$ \mathcal{N} $$ = 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 N $$ \mathcal{N} $$ = 2 SCFTs, therefore they are crucial to understand the Higgs branches of N $$ \mathcal{N} $$ = 2 SCFTs.
ISSN:1029-8479