Kummer surfaces associated with Seiberg-Witten curves
Kummer surfaces associated with Seiberg-Witten curves
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与 Seiberg-Witten 曲线相关的 Kummer 曲面
DOI：
10.1016/j.geomphys.2011.09.010
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发表时间：
2009
影响因子：
1.5
通讯作者：
Andreas Malmendier
中科院分区：
文献类型：
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作者：
Andreas Malmendier
通过对 N=2 超对称纯 SU(2)-规范理论的 Seiberg-Witten 曲线的基曲线 CP1 进行有理变换，我们获得了 Picard 阶 17 的雅可比椭圆 K3 曲面族。将纯 SU(2)-规范理论的 Seiberg-Witten 曲线与 Nf=2 无质量超多重态的 SU(2)-规范理论的 Seiberg-Witten 曲线相关的同源性延伸到定义 Nikulin族中每个 K3 曲面上的对合。我们证明，通过对合对 K3 曲面的商进行去奇异化与属二曲线的雅可比变体的 Kummer 曲面是同构的。然后我们推导出与椭圆 K3 表面相关的 Yukawa 耦合与纯 SU(2)-规范理论的 Yukawa 耦合之间的关系。
By carrying out a rational transformation on the base curve CP1of the Seiberg–Witten curve for N=2 supersymmetric pure SU(2)-gauge theory, we obtain a family of Jacobian elliptic K3 surfaces of Picard rank 17. The isogeny relating the Seiberg–Witten curve for pure SU(2)-gauge theory to the one for SU(2)-gauge theory with Nf=2 massless hypermultiplets extends to define a Nikulin involution on each K3 surface in the family. We show that the desingularization of the quotient of the K3 surface by the involution is isomorphic to a Kummer surface of the Jacobian variety of a curve of genus two. We then derive a relation between the Yukawa coupling associated with the elliptic K3 surface and the Yukawa coupling of pure SU(2)-gauge theory.