论文标题
角色品种和$ su（2）$晶格量规理论i的符号几何形状
Symplectic Geometry of character varieties and $SU(2)$ Lattice Gauge Theory I
论文作者
论文摘要
鉴于有限的连接图$λ$，$ su（2）$ lattice仪表范围的空间是$λ$，modulo量规变换，是一个拉格朗日的submanifold，具有$ su（2）$ themartival- $ su（2）$角色品种（= Chern-simons of Chern-Simons of Chern-Simons Theoper）的相关表面。我们提供的证据表明，在大型$λ$的限制下，相对于liouville测量近似于晶格理论积分的整合。在W. Goldman，L。Jeffrey和J. Weitsman的作品中，Duistermaat-Heckman的形式主义适用于角色的相关积分。 Verlinde代数的连续版本有助于计算。在两个维度中，我们恢复标准表达式。对于三维周期性晶格的理论，我们带有Migdal动作的理论，我们对符号分区函数的表达非常愉快，而Wilson Action的表达式更加详尽。每个都是带有积极术语的系列的总和。一个人还可以写下有关Plaquette-Plaquette相关性和'T Hooft Loops的表达式。
Given a finite connected graph $Λ$, the space of $SU(2)$ lattice gauge-fields on $Λ$, modulo gauge transformations, is a Lagrangian submanifold -- with mild singularities -- of the $SU(2)$ character variety (= phase-space of Chern-Simons theory) of an associated surface. We present evidence that, in the limit of large $Λ$, integration over the character variety with respect to the Liouville measure approximates lattice-theoretic integrals. By the works of W. Goldman, L. Jeffrey and J. Weitsman, the formalism of Duistermaat-Heckman applies to the relevant integrals over the character variety. A continuous version of the Verlinde algebra facilitates computations. In two dimensions we recover standard expressions. For the theory on a 3-dimensional periodic lattice $Λ$ with Migdal action we get a very pleasant expression for the symplectic partition function, and with the Wilson action a more elaborate one. Each is a sum of a series with positive terms. One can also write down expressions for plaquette-plaquette correlations and 't Hooft loops.
