通过自发对称性破缺实现欧氏IKKT矩阵模型额外维数的动态紧化
Dynamical Compactification of Extra Dimensions in the Euclidean IKKT Matrix Model via Spontaneous Symmetry Breaking
摘要：
IKKT矩阵模型已被证明是超弦理论的一个有希望的非微扰形式。在这个模型中，时空从大N极限的微观矩阵自由度中动态地出现，洛伦兹版本的蒙特卡罗模拟提供了一个涌现的（3 + 1）维膨胀时空的证据。在这次演讲中，我们讨论了IKKT矩阵模型的欧几里德版本，并通过10维旋转对称的自发对称性破缺（SSB）提供额外维度动力学紧化的证据。我们使用复朗之万方法（CLM）对一个具有严重复作用问题的系统进行了数值模拟。我们研究了当我们改变变形参数时的单边带斑图，并得出结论：原来的模型具有SO（3）对称真空，这与以前用高斯展开法（GEM）计算的结果一致。我们采用GEM变形模型，我们得到的结果与CLM得到的一致。
英文摘要：
The IKKT matrix model has been conjectured to provide a promising nonperturbative formulation of superstring theory. In this model, spacetime emerges dynamically from the microscopic matrix degrees of freedom in the large-N limit, and Monte Carlo simulations of the Lorentzian version provide evidence of an emergent (3+1)-dimensional expanding space-time. In this talk, we discuss the Euclidean version of the IKKT matrix model and provide evidence of dynamical compactification of the extra dimensions via the spontaneous symmetry breaking (SSB) of the 10D rotational symmetry. We perform numerical simulations of a system with a severe complex action problem by using the complex Langevin method (CLM). The CLM suffers from the singular-drift problem and we deform the model in order to avoid it. We study the SSB pattern as we vary the deformation parameter and we conclude that the original model has an SO(3) symmetric vacuum, in agreement with previous calculations using the Gaussian expansion method (GEM). We employ the GEM to the deformed model and we obtain results consistent with the ones obtained by CLM.
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