作为塞伯格对偶性的福氏 ODEs

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL
Sergio Cecotti
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引用次数: 0

摘要

福氏微分方程的经典理论在很大程度上等同于四元SUSY规理论的塞伯格对偶性理论。特别是:鉴于线性 ODE 与具有 $4$ 超对称性的量规理论之间的字典,所有已知解的积分表示及其连接公式都是塞伯格对偶性(分析上继续)的直接后果。本论文的目的是以物理数学的精神 "物理地 "解释这种非凡的关系。这种联系通过 "镜像理论 "来识别 $\mathbb{P}^1$ 上的不可还原对数连接与 4d $\mathcal{N} = 2 \: SU(2)$ SYM 的可能 BPS dyons(与某种阿基里斯-道格拉斯 "物质 "耦合)。当底层束是微不足道的,即对数连接是一个富克斯系统时,涟的世界线理论就会简化,塞伯格对偶性对富克斯ODE的作用就会变得相当明确。这种对偶作用最好用 Kac-Moody 列代数(及其隶属)的表示理论来描述。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Fuchsian ODEs as Seiberg dualities
The classical theory of Fuchsian differential equations is largely equivalent to the theory of Seiberg dualities for quiver SUSY gauge theories. In particular: all known integral representations of solutions, and their connection formulae, are immediate consequences of (analytically continued) Seiberg duality in view of the dictionary between linear ODEs and gauge theories with $4$ supersymmetries. The purpose of this divertissement is to explain “physically” this remarkable relation in the spirit of Physical Mathematics. The connection goes through a “mirror-theoretic” identification of irreducible logarithmic connections on $\mathbb{P}^1$ with would-be BPS dyons of 4d $\mathcal{N} = 2 \: SU(2)$ SYM coupled to a certain Argyres–Douglas “matter”. When the underlying bundle is trivial, i.e. the log‑connection is a Fuchs system, the world-line theory of the dyon simplifies and the action of Seiberg duality on the Fuchsian ODEs becomes quite explicit. The duality action is best described in terms of Representation Theory of Kac–Moody Lie algebras (and their affinizations).
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来源期刊
Advances in Theoretical and Mathematical Physics
Advances in Theoretical and Mathematical Physics 物理-物理:粒子与场物理
CiteScore
2.20
自引率
6.70%
发文量
0
审稿时长
>12 weeks
期刊介绍: Advances in Theoretical and Mathematical Physics is a bimonthly publication of the International Press, publishing papers on all areas in which theoretical physics and mathematics interact with each other.
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