Mean field approximation of IIB matrix model and emergence of four-dimensional space-time
Mean field approximation of IIB matrix model and emergence of four-dimensional space-time
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IIB矩阵模型的平均场近似与四维时空的出现
DOI：
10.1016/s0550-3213(02)00908-2
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
S. Shinohara
中科院分区：
文献类型：
--
作者：
H. Kawai;S. Kawamoto;T. Kuroki;T. Matsuo;S. Shinohara
为了分析弦理论的非微扰动力学，Nishimura和Sugino将改进的平均场近似(IMFA)应用于IIB矩阵模型。我们提取了IMFA的精髓，得到了一种通用的格式--改进的泰勒展开式，它适用于一大类不一定收敛的级数。在2pi自由能的帮助下，这种近似方案使我们能够进行更高阶的计算。我们证明了自由能的值在高阶是稳定的，这支持了近似的有效性。此外，当我们考虑到更高的阶数时，我们发现“我们的”时空范围与内部空间的范围之间的比率迅速增加。我们的结果表明，在IIB矩阵模型中，四维时空是自发产生的。
For the purpose of analyzing non-perturbative dynamics of string theory, Nishimura and Sugino have applied an improved mean field approximation (IMFA) to IIB matrix model. We have extracted the essence of the IMFA and obtained a general scheme, the improved Taylor expansion, that can be applied to a wide class of series which is not necessarily convergent. This approximation scheme with the help of the 2PI free energy enables us to perform higher order calculations. We have shown that the value of the free energy is stable at higher orders, which supports the validity of the approximation. Moreover, the ratio between the extent of “our” space–time and that of the internal space is found to increase rapidly as we take the higher orders into account. Our results suggest that the four-dimensional space–time emerges spontaneously in IIB matrix model.