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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-04-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP04(2021)271 |
| _version_ | 1818722317138657280 |
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| author | Dan Xie Wenbin Yan |
| author_facet | Dan Xie Wenbin Yan |
| author_sort | Dan Xie |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-17T20:52:42Z |
| format | Article |
| id | doaj.art-da71321fded94e77a486e265012872d1 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-17T20:52:42Z |
| publishDate | 2021-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-da71321fded94e77a486e265012872d12022-12-21T21:32:58ZengSpringerOpenJournal of High Energy Physics1029-84792021-04-012021415710.1007/JHEP04(2021)2714d N $$ \mathcal{N} $$ = 2 SCFTs and lisse W-algebrasDan Xie0Wenbin Yan1Yau Mathematics Science center, Tsinghua UniversityYau Mathematics Science center, Tsinghua UniversityAbstract 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.https://doi.org/10.1007/JHEP04(2021)271Supersymmetric Gauge TheorySupersymmetry and Duality |
| spellingShingle | Dan Xie Wenbin Yan 4d N $$ \mathcal{N} $$ = 2 SCFTs and lisse W-algebras Journal of High Energy Physics Supersymmetric Gauge Theory Supersymmetry and Duality |
| title | 4d N $$ \mathcal{N} $$ = 2 SCFTs and lisse W-algebras |
| title_full | 4d N $$ \mathcal{N} $$ = 2 SCFTs and lisse W-algebras |
| title_fullStr | 4d N $$ \mathcal{N} $$ = 2 SCFTs and lisse W-algebras |
| title_full_unstemmed | 4d N $$ \mathcal{N} $$ = 2 SCFTs and lisse W-algebras |
| title_short | 4d N $$ \mathcal{N} $$ = 2 SCFTs and lisse W-algebras |
| title_sort | 4d n mathcal n 2 scfts and lisse w algebras |
| topic | Supersymmetric Gauge Theory Supersymmetry and Duality |
| url | https://doi.org/10.1007/JHEP04(2021)271 |
| work_keys_str_mv | AT danxie 4dnmathcaln2scftsandlissewalgebras AT wenbinyan 4dnmathcaln2scftsandlissewalgebras |