论文标题
Quiver仪表理论：超越反射性
Quiver Gauge Theories: Beyond Reflexivity
论文作者
论文摘要
反身多边形已在数学和物理学的各种情况下进行了广泛的研究。我们通过查看具有两个内部点的45个不同的晶格多边形来概括这个程序，直到SL（2，2，$ \ Mathbb {z} $）等价。每个都对应于Sasaki-Einstein上的圆锥体3倍的一些仿生曲面，为5倍。我们研究了探测这些锥体的D3-branes的Quiver仪表，这些理论与中间模量空间一致。 Sasaki-Einstein碱歧管的最小体积函数在计算R-earduges中起着重要作用。我们分析了这些最小化体积相对于由多边形构成的拓扑量的紧凑型表面。与反射性多面体不同，一个可以从两个内部点中有两个风扇，因此在完成分辨率后产生了两个平滑品种，从而导致了一对有趣的紧密相关的几何形状和衡量理论。
Reflexive polygons have been extensively studied in a variety of contexts in mathematics and physics. We generalize this programme by looking at the 45 different lattice polygons with two interior points up to SL(2,$\mathbb{Z}$) equivalence. Each corresponds to some affine toric 3-fold as a cone over a Sasaki-Einstein 5-fold. We study the quiver gauge theories of D3-branes probing these cones, which coincide with the mesonic moduli space. The minimum of the volume function of the Sasaki-Einstein base manifold plays an important role in computing the R-charges. We analyze these minimized volumes with respect to the topological quantities of the compact surfaces constructed from the polygons. Unlike reflexive polytopes, one can have two fans from the two interior points, and hence give rise to two smooth varieties after complete resolutions, leading to an interesting pair of closely related geometries and gauge theories.
