Moduli spaces of gauge theories from Dimer models: proof of the correspondence
Moduli spaces of gauge theories from Dimer models: proof of the correspondence
复制标题
二聚体模型规范理论的模空间：对应性证明
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
David Vegh
中科院分区：
文献类型：
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作者：
S. Franco;David Vegh
最近，一种新的方法来推导的模空间的规范理论，产生的世界体积的D3-膜探测奇异复曲面的卡-丘锥。根据该提议，规范理论的规范群、物质含量和树级超势被编码在一个周期性的平铺结构中，即二聚体图。该猜想提供了一个简单的程序，以确定模空间的规范理论的完美匹配。对于规范理论所描述的周期颤动，可以嵌入在一个二维环面，我们证明了与规范的线性西格玛模型和计算的特征多项式的二聚体模型的牛顿多边形的环面模空间的测定之间的等价性。我们证明了完美匹配与线性sigma模型中的场是一一对应的。进一步证明了每一个σ模型场在复曲面图中的位置都是由相应的完美匹配的高度函数的斜率给出的。
Recently, a new way of deriving the moduli space of quiver gauge theories that arise on the world–volume of D3–branes probing singular toric Calabi–Yau cones was conjectured. According to the proposal, the gauge group, matter content and tree–level superpotential of the gauge theory is encoded in a periodic tiling, the dimer graph. The conjecture provides a simple procedure for determining the moduli space of the gauge theory in terms of perfect matchings. For gauge theories described by periodic quivers that can be embedded on a two–dimensional torus, we prove the equivalence between the determination of the toric moduli space with a gauged linear sigma model and the computation of the Newton polygon of the characteristic polynomial of the dimer model. We show that perfect matchings are in one–to–one correspondence with fields in the linear sigma model. Furthermore, we prove that the position in the toric diagram of every sigma model field is given by the slope of the height function of the corresponding perfect matching.