论文标题
Quiver Vortex Moduli空间的音量
The Volume of the Quiver Vortex Moduli Space
论文作者
论文摘要
我们研究紧凑型黎曼表面的箭量规定中BPS涡流的模量空间体积。 BPS涡流的存在对箭袋理论施加了约束。我们表明，模量空间体积是由适当的同胞运算符（体积操作员）的VEV给出的，其中涡旋式仪表理论是嵌入涡流的BPS方程。在超对称仪表理论中，使用定位将模量空间体积精确地评估为轮廓积分。图理论可用于构建超对称箭量计理论并得出体积公式。体积的轮廓积分公式（Jeffrey-Kirwan残基公式的概括）导致Bradlow边界（涡旋上的涡度上限由Riemann表面的面积除以涡旋的内在尺寸）。我们提供了各种颤抖理论的一些示例，并讨论了这些理论中模量空间体积的属性。我们的公式应用于具有$ cp^n $目标空间的测量的非线性Sigma模型中的Vortex模量空间的体积，这是由父Quiver仪表理论的强耦合限制获得的。我们还讨论了对箭量规程理论和体积公式的“阿贝利安化”的非 - 亚伯利亚概括。
We study the moduli space volume of BPS vortices in quiver gauge theories on compact Riemann surfaces. The existence of BPS vortices imposes constraints on the quiver gauge theories. We show that the moduli space volume is given by a vev of a suitable cohomological operator (volume operator) in a supersymmetric quiver gauge theory, where BPS equations of the vortices are embedded. In the supersymmetric gauge theory, the moduli space volume is exactly evaluated as a contour integral by using the localization. Graph theory is useful to construct the supersymmetric quiver gauge theory and to derive the volume formula. The contour integral formula of the volume (generalization of the Jeffrey-Kirwan residue formula) leads to the Bradlow bounds (upper bounds on the vorticity by the area of the Riemann surface divided by the intrinsic size of the vortex). We give some examples of various quiver gauge theories and discuss properties of the moduli space volume in these theories. Our formula are applied to the volume of the vortex moduli space in the gauged non-linear sigma model with $CP^N$ target space, which is obtained by a strong coupling limit of a parent quiver gauge theory. We also discuss a non-Abelian generalization of the quiver gauge theory and "Abelianization" of the volume formula.
