Special arithmetic of flavor
Abstract We revisit the classification of rank-1 4d N=2 $$ \mathcal{N}=2 $$ QFTs in the spirit of Diophantine Geometry, viewing their special geometries as elliptic curves over the chiral ring (a Dedekind domain). The Kodaira-Néron model maps the space of non-trivial rank-1 special geometries to the...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-08-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP08(2018)057 |
| _version_ | 1818955955297058816 |
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| author | Matteo Caorsi Sergio Cecotti |
| author_facet | Matteo Caorsi Sergio Cecotti |
| author_sort | Matteo Caorsi |
| collection | DOAJ |
| description | Abstract We revisit the classification of rank-1 4d N=2 $$ \mathcal{N}=2 $$ QFTs in the spirit of Diophantine Geometry, viewing their special geometries as elliptic curves over the chiral ring (a Dedekind domain). The Kodaira-Néron model maps the space of non-trivial rank-1 special geometries to the well-known moduli of pairs (ε, F ∞) where E is a relatively minimal, rational elliptic surface with section, and F ∞ a fiber with additive reduction. Requiring enough Seiberg-Witten differentials yields a condition on (ε, F ∞) equivalent to the “safely irrelevant conjecture”. The Mordell-Weil group of E (with the Néron-Tate pairing) contains a canonical root system arising from (−1)-curves in special position in the Néron-Severi group. This canonical system is identified with the roots of the flavor group F: the allowed flavor groups are then read from the Oguiso-Shioda table of Mordell-Weil groups. Discrete gaugings correspond to base changes. Our results are consistent with previous work by Argyres et al. |
| first_indexed | 2024-12-20T10:46:17Z |
| format | Article |
| id | doaj.art-eb708f7b69544b3c9a700cf07fe9c20b |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-20T10:46:17Z |
| publishDate | 2018-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-eb708f7b69544b3c9a700cf07fe9c20b2022-12-21T19:43:24ZengSpringerOpenJournal of High Energy Physics1029-84792018-08-012018813910.1007/JHEP08(2018)057Special arithmetic of flavorMatteo Caorsi0Sergio Cecotti1SISSASISSAAbstract We revisit the classification of rank-1 4d N=2 $$ \mathcal{N}=2 $$ QFTs in the spirit of Diophantine Geometry, viewing their special geometries as elliptic curves over the chiral ring (a Dedekind domain). The Kodaira-Néron model maps the space of non-trivial rank-1 special geometries to the well-known moduli of pairs (ε, F ∞) where E is a relatively minimal, rational elliptic surface with section, and F ∞ a fiber with additive reduction. Requiring enough Seiberg-Witten differentials yields a condition on (ε, F ∞) equivalent to the “safely irrelevant conjecture”. The Mordell-Weil group of E (with the Néron-Tate pairing) contains a canonical root system arising from (−1)-curves in special position in the Néron-Severi group. This canonical system is identified with the roots of the flavor group F: the allowed flavor groups are then read from the Oguiso-Shioda table of Mordell-Weil groups. Discrete gaugings correspond to base changes. Our results are consistent with previous work by Argyres et al.http://link.springer.com/article/10.1007/JHEP08(2018)057Conformal Field TheoryExtended SupersymmetrySupersymmetric Gauge TheorySupersymmetry and Duality |
| spellingShingle | Matteo Caorsi Sergio Cecotti Special arithmetic of flavor Journal of High Energy Physics Conformal Field Theory Extended Supersymmetry Supersymmetric Gauge Theory Supersymmetry and Duality |
| title | Special arithmetic of flavor |
| title_full | Special arithmetic of flavor |
| title_fullStr | Special arithmetic of flavor |
| title_full_unstemmed | Special arithmetic of flavor |
| title_short | Special arithmetic of flavor |
| title_sort | special arithmetic of flavor |
| topic | Conformal Field Theory Extended Supersymmetry Supersymmetric Gauge Theory Supersymmetry and Duality |
| url | http://link.springer.com/article/10.1007/JHEP08(2018)057 |
| work_keys_str_mv | AT matteocaorsi specialarithmeticofflavor AT sergiocecotti specialarithmeticofflavor |