We revisit the classification of rank-1 4d 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.

Special arithmetic of flavor / Caorsi, M.; Cecotti, S.. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - 2018:8(2018), pp. 1-38. [10.1007/JHEP08(2018)057]

Special arithmetic of flavor

Caorsi M.;Cecotti S.
2018

Abstract

We revisit the classification of rank-1 4d 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.
2018
8
1
38
057
https://doi.org/10.1007/JHEP08(2018)057
https://arxiv.org/abs/1803.00531
Caorsi, M.; Cecotti, S.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/98105
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