论文标题
紫红色作为塞伯格二元性
Fuchsian ODEs as Seiberg dualities
论文作者
论文摘要
紫红色差分方程的经典理论在很大程度上等同于Quiver Susy Gauge理论的Seiberg二元性理论。特别是：鉴于线性ODES和衡量理论之间具有4个超对称性的词典，所有已知的解决方案及其连接公式的所有已知积分表示及其连接公式是Seiberg二元性的直接后果。 这种转移的目的是在物理数学精神上解释“物理上”这种显着的关系。该连接通过$ \ mathbb {p}^1 $ bps bps bps bps dyons a $ \ nd $ \ natcal symcal {$ \ n} $ s $ sy（2）= 2）的“镜像理论”识别不可约束的对数连接的标识（p}^1 $） “物质'。当底层捆绑琐碎时，即对数连接是一个福克斯系统时，dyon的世界线理论简化了，塞伯格二重性对fuchsian odes的作用就变得很明确。二元行动是在kac-moody lie lie algeberaS的代表理论及其altgebras的代表方面所描述的。
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).
