标题： 曲率矩阵模型用于动态三角剖分和Itzykson-DiFrancesco公式 显示英文标题

标题： Curvature Matrix Models for Dynamical Triangulations and the Itzykson-DiFrancesco Formula

摘要： 我们使用特征展开技术研究了一类双权三角随机曲面的矩阵模型在大N极限下的性质。 我们证明，对于动态三角剖分顶点权重的各种选择，可以通过对Itzykson-Di Francesco公式在模三的Young表权重同余类上重新求和来求解该模型。 由此我们表明，大N极限暗示了与仅用偶数配位数顶点加权的随机曲面模型之间的非平凡对应关系。 我们检查了所有模型中的临界行为和可观测量的计算，并讨论了它们之间的相互关系。 我们得到了顶点权重选择简单的模型的显式解，并利用它们来展示矩阵模型如何再现随机曲面求和的特性。 我们还讨论了大N特征展开方法的一些一般性质以及我们结果的潜在物理应用。 显示英文摘要

摘要： We study the large-N limit of a class of matrix models for dually weighted triangulated random surfaces using character expansion techniques. We show that for various choices of the weights of vertices of the dynamical triangulation the model can be solved by resumming the Itzykson-Di Francesco formula over congruence classes of Young tableau weights modulo three. From this we show that the large-N limit implies a non-trivial correspondence with models of random surfaces weighted with only even coordination number vertices. We examine the critical behaviour and evaluation of observables and discuss their interrelationships in all models. We obtain explicit solutions of the model for simple choices of vertex weightings and use them to show how the matrix model reproduces features of the random surface sum. We also discuss some general properties of the large-N character expansion approach as well as potential physical applications of our results.