arXiv 2006.007682020-06-01hep-lathep-th

洛伦兹型IIB矩阵模型中（3+1）维膨胀时空出现的新观点

New perspectives on the emergence of (3+1)D expanding space-time in the Lorentzian type IIB matrix model

Jun Nishimura

备注：: 15 pages, 2 figures, Contribution to the proceedings of the Corfu Summer Institute 2019 "School and Workshops on Elementary Particle Physics and Gravity" (CORFU2019), 31 August - 25 September 2019, Corfu, Greece, based on arXiv:1904.05919 [hep-th] and arXiv:1802.01876 [hep-lat]

摘要：

IIB型矩阵模型是超弦理论非微扰形式的一个有希望的候选者。特别是在洛仑兹版本中，（3+1）维膨胀时空的出现是通过对这个模型的蒙特卡罗研究观察到的。在这里，我们提供了新的观点（3+1）D扩展的时空，从最近的研究已经出现。首先，它被发现，由模拟生成的矩阵配置是奇异的，在表示扩展的3D空间的子矩阵只有两个大的特征值与泡利矩阵。由于在模拟模型时为了避免符号问题而使用了近似，因此避免了这个问题的发生。为了证实这一猜想，复朗之万方法被用来克服符号问题，而不是使用近似。结果确实显示出明显偏离Pauli矩阵结构，而（3+1）D膨胀行为保持不变。在一定的时间尺度内得到的经典解一般表现为具有光滑时空结构的（3+1）维膨胀行为。

英文摘要：

The type IIB matrix model is a promising candidate for a nonperturbative formulation of superstring theory. In the Lorentzian version, in particular, the emergence of (3+1)D expanding space-time was observed by Monte Carlo studies of this model. Here we provide new perspectives on the (3+1)D expanding space-time that have arised from recent studies. First it was found that the matrix configurations generated by the simulation are singular in that the submatrices representing the expanding 3D space have only two large eigenvalues associated with the Pauli matrices. This problem was conjectured to occur due to the approximation used to avoid the sign problem in simulating the model. In order to confirm this conjecture, the complex Langevin method was applied to overcome the sign problem instead of using the approximation. The results indeed showed a clear departure from the Pauli-matrix structure, while the (3+1)D expanding behavior remained unaltered. It was also found that classical solutions obtained within a certain ansatz show quite generically a (3+1)D expanding behavior with smooth space-time structure.

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