Seiberg-Witten curve for E string theory revisited
Seiberg-Witten curve for E string theory revisited
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重新审视 E 弦理论的 Seiberg-Witten 曲线
DOI：
10.1143/ptps.152.15
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发表时间：
2002
影响因子：
1.5
通讯作者：
K. Sakai
中科院分区：
文献类型：
--
作者：
T. Eguchi;K. Sakai
我们讨论了最近在第0203025号论文中得到的E弦理论的Seiberg-Witten曲线的各种性质。E弦的Seiberg-Witten曲线描述了在R4 × T2上紧化的六维（1，0）超对称理论的低能动力学.它具有明显的仿射E8整体对称性，模为τ，E8 Wilson线参数为{mi}，i = 1，2，. . .，8，它们与有理椭圆曲面的几何相关联。当环面T2的半径R5，R6退化为R5，R6 → 0时，E弦曲线退化为已知的四维和五维规范理论的Seiberg-Witten曲线.本文首先研究了有理椭圆曲面的几何性质，并确定了Wilson线参数的几何意义。通过微调这些参数，我们还研究了我们的曲线对应于各种未破缺对称群的退化。我们还发现了一种新的方法，减少到四维理论，而不采取退化限制的T2，使SL（2，Z）对称性是原封不动的。通过对Wilson线参数进行特殊的设置，我们得到了具有4种味道的四维SU（2）Seiberg-维滕理论，以及Donagi和维滕给出的描述扰动N = 4理论动力学的曲线.
We discuss various properties of the Seiberg–Witten curve for the E-string theory which we have obtained recently in hep-th/0203025. Seiberg–Witten curve for the E-string describes the low-energy dynamics of a six-dimensional (1,0) SUSY theory when compactified on R 4 × T 2 . It has a manifest affineE8 global symmetry with modulus τ and E8 Wilson line parameters {mi}, i = 1,2, . . . ,8 which are associated with the geometry of the rational elliptic surface. When the radii R5, R6 of the torus T 2 degenerate R5, R6 → 0, E-string curve is reduced to the known Seiberg–Witten curves of four- and five-dimensional gauge theories. In this paper we first study the geometry of rational elliptic surface and identify the geometrical significance of the Wilson line parameters. By fine tuning these parameters we also study degenerations of our curve corresponding to various unbroken symmetry groups. We also find a new way of reduction to four-dimensional theories without taking a degenerate limit of T 2 so that the SL(2, Z) symmetry is left intact. By setting some of the Wilson line parameters to special values we obtain the four-dimensional SU(2) Seiberg–Witten theory with 4 flavors and also a curve by Donagi and Witten describing the dynamics of a perturbed N = 4 theory.