论文标题
高斯BFSS矩阵模型的蒙特卡洛模拟大量尺寸
Monte-Carlo simulation of the Gaussian BFSS matrix model at large number of dimensions
论文作者
论文摘要
在本论文中，我们使用基于Metropolis算法的Monte Carlo模拟研究了BFSS矩阵模型的玻色子部分的高斯近似值。我们精确地重现了从限制（黑色字符串）相到反封码（黑洞）相的丝状Hagedorn相过渡。我们使用Polyakov环作为订单参数来研究该模型在不同温度下的大N行为，还计算了其他可观察到的内部能量和空间范围。在最后一部分中，我们将矩阵几何方法介绍了修改的动作，在该方法中，我们仅捕获了几何Yang-Mills的残余到一个婴儿模糊的球相，其中模糊的球形溶液仅表现为三个切割构型。杨米尔斯相保留了其大多数特征，有两个例外：i）实心球内的均匀分布以很小的量规耦合常数与Wigner的半圆形定律的次数遭受分频，而ii）小t的均匀分布不存在。
In this thesis, we studied a Gaussian approximation to the bosonic part of the BFSS matrix model using Monte Carlo simulations based on the Metropolis algorithm. We reproduce with great accuracy the stringy Hagedorn phase transition from a confinement (black string) phase to a deconfinement (black hole) phase. We used the Polyakov loop as an order parameter to investigate the large-N behavior of this model at different temperatures, other observables such as internal energy and extent of space were also computed. In the last part, we present the matrix-geometry approach to a modified action where we captured only a remnant of the geometric Yang-Mills to a baby-fuzzy-sphere phase where the fuzzy sphere solution is only manifested as a three-cut configuration. The Yang-Mills phase retains most of its characteristics with two exceptions: i) the uniform distribution inside a solid ball suffers a crossover at very small values of the gauge coupling constant to a Wigner's semi-circle law, and ii) the uniform distribution at small T is non-existent.
