| Autor: |
Sergio Cecotti |
| Jazyk: |
angličtina |
| Rok vydání: |
2024 |
| Předmět: |
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| Zdroj: |
Journal of High Energy Physics, Vol 2024, Iss 7, Pp 1-38 (2024) |
| Druh dokumentu: |
article |
| ISSN: |
1029-8479 |
| DOI: |
10.1007/JHEP07(2024)020 |
| Popis: |
Abstract The Weil correspondence states that the datum of a Seiberg-Witten differential is equivalent to an algebraic group extension of the integrable system associated to the Seiberg-Witten geometry. Remarkably this group extension represents quantum consistent couplings for the N $$ \mathcal{N} $$ = 2 QFT if and only if the extension is anti-affine in the algebro-geometric sense. The universal special geometry is the algebraic integrable system whose Lagrangian fibers are the anti-affine extension groups; it is defined over a base B $$ \mathcal{B} $$ parametrized by the Coulomb coordinates and the couplings. On the total space of the universal geometry there is a canonical (holomorphic) Euler differential. The ordinary Seiberg-Witten geometries at fixed couplings are symplectic quotients of the universal one, and the Seiberg-Witten differential arises as the reduction of the Euler one in accordance with the Weil correspondence. This universal viewpoint allows to study geometrically the flavor symmetry of the N $$ \mathcal{N} $$ = 2 SCFT in terms of the Mordell-Weil lattice (with Néron-Tate height) of the Albanese variety A L $$ {A}_{\mathbbm{L}} $$ of the universal geometry seen as a quasi-Abelian variety Y L $$ {Y}_{\mathbbm{L}} $$ defined over the function field L ≡ ℂ B $$ \mathbbm{L}\equiv \mathbb{C}\left(\mathcal{B}\right) $$ . |
| Databáze: |
Directory of Open Access Journals |
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