欧几里德IKKT矩阵模型中10维旋转对称自发破缺的复朗之万分析
Complex Langevin analysis of the spontaneous breaking of 10D rotational symmetry in the Euclidean IKKT matrix model
摘要：
IKKT矩阵模型是超弦理论的非微扰表述的一个有希望的候选者，在超弦理论中，时空被约束为在大$N$极限下从微观矩阵自由度动态地出现。事实上，在洛伦兹版本中，蒙特卡罗研究表明（3+1）维膨胀时空的出现。在这里，我们研究的欧几里德版本，而不是通过自发对称性破缺（SSB）的10维旋转对称的额外的维度的动力学紧化的另一种方案进行调查。我们进行数值模拟的基础上，复杂的朗之万方法（CLM），以避免严重的符号问题。此外，为了避免CLM中的奇异漂移问题，我们变形的模型，并确定SSB模式，因为我们改变变形参数。从这些结果中，我们得出结论，原来的模型具有SO（3）对称真空，这是与以前的结果一致的高斯展开方法（GEM）。我们还将GEM应用到变形矩阵模型中，并发现与CLM得到的结果一致。
英文摘要：
The IKKT matrix model is a promising candidate for a nonperturbative formulation of superstring theory, in which spacetime is conjectured to emerge dynamically from the microscopic matrix degrees of freedom in the large-$N$ limit. Indeed in the Lorentzian version, Monte Carlo studies suggested the emergence of (3+1)-dimensional expanding space-time. Here we study the Euclidean version instead, and investigate an alternative scenario for dynamical compactification of extra dimensions via the spontaneous symmetry breaking (SSB) of 10D rotational symmetry. We perform numerical simulations based on the complex Langevin method (CLM) in order to avoid a severe sign problem. Furthermore, in order to avoid the singular-drift problem in the CLM, we deform the model and determine the SSB pattern as we vary the deformation parameter. From these results, we conclude that the original model has an SO(3) symmetric vacuum, which is consistent with previous results obtained by the Gaussian expansion method (GEM). We also apply the GEM to the deformed matrix model and find consistency with the results obtained by the CLM.
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