2019/10/05 by Dan Xie, Wenbin Yan, Xie, Dan +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT) #hep-th #math-ph #math.MP #math.QA #math.RT
paper · pdf · doi:10.48550/arxiv.1910.02281
55 pages, 8 figures, 23 tables
arxiv created 2019/10/05 · openalex publication_date 2019/10/05 · arxiv updated 2019/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We continue our studies of the correspondence between 4d 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 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=2 SCFTs, therefore they are crucial to understand the Higgs branches of N=2 SCFTs.