论文标题
BFSS和IKKT矩阵模型的蒙特卡洛模拟
Monte Carlo Simulations of BFSS and IKKT Matrix Models
论文作者
论文摘要
在本论文中，我们使用蒙特卡洛模拟研究了骨气BFSS和IKKT矩阵模型。首先，我们探索了一些玩具模型来检查数值模拟的有效性。然后，我们使用汉密尔顿蒙特卡洛（HMC）算法模拟了BFSS矩阵模型。在BFSS矩阵模型中，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。我们的模拟证实，随着系统温度的变化，该模型表现出限制 - 结构相变。除了Polyakov循环外，还计算了其他可观察到的内部能量和空间范围。在Bosonic IKKT模型中，我们使用惯性张量的矩研究了SO（10）对称的自发对称性破坏（SSB），并发现该模型中没有SO（10）对称性的SSB。除了惯性张量时刻的特征值外，还计算了其他可观察到的时空范围。我们还研究了相位的IKKT模型的仿真理论。
In this thesis, we studied the bosonic BFSS and IKKT matrix models using Monte Carlo simulations. First, we explored some toy models to check the validity of the numerical simulations. Then we simulated the BFSS matrix model using Hamiltonian Monte Carlo (HMC) algorithm. In the BFSS matrix model, we used the Polyakov loop as an order parameter to investigate the large-N behaviour of this model at different temperatures. Our simulations confirmed that the model exhibits a confinement-deconfinement phase transition as the temperature of the system is varied. Besides the Polyakov loop, other observables such as internal energy and extent of space were also computed. In the bosonic IKKT model, we studied the spontaneous symmetry breaking (SSB) of SO(10) symmetry using the moment of inertia tensor and found that there is no SSB of SO(10) symmetry in this model. Besides the eigenvalues of the moment of inertia tensor, other observable such as extent of spacetime was also computed. We also studied the simulation theory of the phase-quenched IKKT model.
