Dynamical aspects of large- N reduced models
Dynamical aspects of large- N reduced models
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大 N 简化模型的动力学方面
DOI：
10.1016/s0550-3213(99)00056-5
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
A. Tsuchiya
中科院分区：
文献类型：
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作者：
T. Hotta;J. Nishimura;A. Tsuchiya
我们研究了D维Yang-Mills理论的大N约化模型，特别关注与IIB矩阵模型中时空坐标对应的N × N矩阵的本征值有关的动力学问题.我们首先用微扰论的方法给时空的范围设定一个上界。我们进行了蒙特卡罗模拟，并表明上限实际上是饱和的。阐明了我们的结果与Eguchi-Kawai模型中U（1）D对称性的单边带的关系。我们定义了一个表示时空坐标不确定性的量，并证明它与时空的范围具有相同的量级，这意味着经典时空图像被最大限度地破坏了。我们开发了一个1/D的扩展，这使我们能够计算模型的相关函数解析。的洛伦兹不变性的SSB的情况下所示的Monte Carlo模拟以及1/D的扩展。
We study the large-N reduced model of D-dimensional Yang-Mills theory with special attention to dynamical aspects related to the eigenvalues of the N × N matrices, which correspond to the space-time coordinates in the IIB matrix model. We first put an upper bound on the extent of space-time by perturbative arguments. We perform a Monte Carlo simulation and show that the upper bound is actually saturated. The relation of our result to the SSB of the U(1)Dsymmetry in the Eguchi-Kawai model is clarified. We define a quantity which represents the uncertainty of the space-time coordinates and show that it is of the same order as the extent of space-time, which means that a classical space-time picture is maximally broken. We develop a 1/D expansion, which enables us to calculate correlation functions of the model analytically. The absence of an SSB of the Lorentz invariance is shown by the Monte Carlo simulation as well as by the 1/D expansion.