论文标题
欧几里得IKKT矩阵模型中10D旋转对称性自发断裂的复杂Langevin分析
Complex Langevin analysis of the spontaneous breaking of 10D rotational symmetry in the Euclidean IKKT matrix model
论文作者
论文摘要
IKKT矩阵模型是对超弦理论的非扰动公式的有前途的候选者，在该理论中，时空猜想是从显微镜矩阵自由度中动态地出现的，这一数字在很大程度上是$ n $限制的。实际上，在洛伦兹版本中，蒙特卡洛研究表明（3+1）维度扩展时空的出现。在这里，我们改为研究欧几里得版本，并研究通过10D旋转对称性的自发对称性断裂（SSB）动态压实的替代情况。我们基于复杂的Langevin方法（CLM）执行数值模拟，以避免严重的符号问题。此外，为了避免CLM中的单数饮用问题，我们将模型变形并确定SSB模式，因为我们改变了变形参数。从这些结果中，我们得出的结论是，原始模型具有SO（3）对称真空，这与先前通过高斯膨胀方法（GEM）获得的结果一致。我们还将GEM应用于变形的矩阵模型，并与CLM获得的结果保持一致性。
The IKKT matrix model is a promising candidate for a nonperturbative formulation of superstring theory, in which spacetime is conjectured to emerge dynamically from the microscopic matrix degrees of freedom in the large-$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.
