Special arithmetic of flavor
Special arithmetic of flavor
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风味特殊算法
DOI：
10.1007/jhep08(2018)057
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发表时间：
2018
影响因子：
5.4
通讯作者：
S. Cecotti
中科院分区：
文献类型：
--
作者：
Matteo Caorsi;S. Cecotti
We revisit the classification of rank-1 4d N=2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N}=2 $$\end{document} 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.
We revisit the classification of rank-1 4d N=2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N}=2 $$\end{document} 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.