On geometric classification of 5d SCFTs
Abstract We formulate geometric conditions necessary for engineering 5d superconformal field theories (SCFTs) via M-theory compactification on a local Calabi-Yau 3-fold. Extending the classification of the rank 1 cases, which are realized geometrically as shrinking del Pezzo surfaces embedded in a 3...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2018-04-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP04(2018)103 |
| _version_ | 1818108536642600960 |
|---|---|
| author | Patrick Jefferson Sheldon Katz Hee-Cheol Kim Cumrun Vafa |
| author_facet | Patrick Jefferson Sheldon Katz Hee-Cheol Kim Cumrun Vafa |
| author_sort | Patrick Jefferson |
| collection | DOAJ |
| description | Abstract We formulate geometric conditions necessary for engineering 5d superconformal field theories (SCFTs) via M-theory compactification on a local Calabi-Yau 3-fold. Extending the classification of the rank 1 cases, which are realized geometrically as shrinking del Pezzo surfaces embedded in a 3-fold, we propose an exhaustive classification of local 3-folds engineering rank 2 SCFTs in 5d. This systematic classification confirms that all rank 2 SCFTs predicted using gauge theoretic arguments can be realized as consistent theories, with the exception of one family which is shown to be non-perturbatively inconsistent and thereby ruled out by geometric considerations. We find that all rank 2 SCFTs descend from 6d (1,0) SCFTs compactified on a circle possibly twisted with an automorphism together with holonomies for global symmetries around the Kaluza-Klein circle. These results support our conjecture that every 5d SCFT can be obtained from the circle compactification of some parent 6d (1,0) SCFT. |
| first_indexed | 2024-12-11T02:16:55Z |
| format | Article |
| id | doaj.art-1d2a4999ac5e4500911a15368c4d5f4c |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-11T02:16:55Z |
| publishDate | 2018-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-1d2a4999ac5e4500911a15368c4d5f4c2022-12-22T01:24:10ZengSpringerOpenJournal of High Energy Physics1029-84792018-04-012018417510.1007/JHEP04(2018)103On geometric classification of 5d SCFTsPatrick Jefferson0Sheldon Katz1Hee-Cheol Kim2Cumrun Vafa3Jefferson Physical Laboratory, Harvard UniversityDepartment of Mathematics, University of Illinois at Urbana-ChampaignJefferson Physical Laboratory, Harvard UniversityJefferson Physical Laboratory, Harvard UniversityAbstract We formulate geometric conditions necessary for engineering 5d superconformal field theories (SCFTs) via M-theory compactification on a local Calabi-Yau 3-fold. Extending the classification of the rank 1 cases, which are realized geometrically as shrinking del Pezzo surfaces embedded in a 3-fold, we propose an exhaustive classification of local 3-folds engineering rank 2 SCFTs in 5d. This systematic classification confirms that all rank 2 SCFTs predicted using gauge theoretic arguments can be realized as consistent theories, with the exception of one family which is shown to be non-perturbatively inconsistent and thereby ruled out by geometric considerations. We find that all rank 2 SCFTs descend from 6d (1,0) SCFTs compactified on a circle possibly twisted with an automorphism together with holonomies for global symmetries around the Kaluza-Klein circle. These results support our conjecture that every 5d SCFT can be obtained from the circle compactification of some parent 6d (1,0) SCFT.http://link.springer.com/article/10.1007/JHEP04(2018)103Conformal Field Models in String TheoryDifferential and Algebraic GeometryField Theories in Higher DimensionsSupersymmetry and Duality |
| spellingShingle | Patrick Jefferson Sheldon Katz Hee-Cheol Kim Cumrun Vafa On geometric classification of 5d SCFTs Journal of High Energy Physics Conformal Field Models in String Theory Differential and Algebraic Geometry Field Theories in Higher Dimensions Supersymmetry and Duality |
| title | On geometric classification of 5d SCFTs |
| title_full | On geometric classification of 5d SCFTs |
| title_fullStr | On geometric classification of 5d SCFTs |
| title_full_unstemmed | On geometric classification of 5d SCFTs |
| title_short | On geometric classification of 5d SCFTs |
| title_sort | on geometric classification of 5d scfts |
| topic | Conformal Field Models in String Theory Differential and Algebraic Geometry Field Theories in Higher Dimensions Supersymmetry and Duality |
| url | http://link.springer.com/article/10.1007/JHEP04(2018)103 |
| work_keys_str_mv | AT patrickjefferson ongeometricclassificationof5dscfts AT sheldonkatz ongeometricclassificationof5dscfts AT heecheolkim ongeometricclassificationof5dscfts AT cumrunvafa ongeometricclassificationof5dscfts |