来自矩阵的随机体积
Random volumes from matrices
摘要：
我们提出了一类产生三维随机体积的模型，其中每个配置由沿着多个铰链胶合在一起的三角形组成。该模型以矩阵作为动力学变量，用半单结合代数A刻画。虽然大多数的图表示的配置，这不是流形，我们表明，一组可能的图可以大大减少，使只有（和所有的）三维流形与四面体分解出现，通过引入一个颜色结构，并采取适当的大N限制。我们研究了A是矩阵环或群环时模型的解析性质，并证明了矩阵环模型具有一种新的强弱对偶性，这种对偶性互换了三角形和铰链的角色.我们还对我们的模型与色张量模型的关系作了简要的评论。
英文摘要：
We propose a class of models which generate three-dimensional random volumes, where each configuration consists of triangles glued together along multiple hinges. The models have matrices as the dynamical variables and are characterized by semisimple associative algebras A. Although most of the diagrams represent configurations which are not manifolds, we show that the set of possible diagrams can be drastically reduced such that only (and all of the) three-dimensional manifolds with tetrahedral decompositions appear, by introducing a color structure and taking an appropriate large N limit. We examine the analytic properties when A is a matrix ring or a group ring, and show that the models with matrix ring have a novel strong-weak duality which interchanges the roles of triangles and hinges. We also give a brief comment on the relationship of our models with the colored tensor models.
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