arXiv 1607.082962016-07-29hep-thhep-lat

$4$维中的涌现模糊几何与模糊物理

Emergent fuzzy geometry and fuzzy physics in $4$ dimensions

Badis Ydri, Rouag Ahlam, Ramda Khaled

备注：: 45 pages, 18 figures; v2: very minor corrections
DOI：: 10.1016/j.nuclphysb.2017.01.023

摘要：

本文用Monte Carlo方法详细计算了具有四次质量变形的三维和六维IKKT Yang-Mills矩阵模型的相图。背景紧急模糊几何在二维和四维观察到的波动给出的非交换$U(1)$规范理论非常弱耦合到正常的标量场。动态确定的几何形状分别由模糊球${\bf S}^2_N$和${\bf S}^2_N\times{\bf S}^2_N$给出。这三种和六种矩阵模型属于同一普适类，但存在一定的差异。例如，在二维中，几何是完全稳定的，而在四维中，几何仅在极限$M\longrightarrow \infty$中是稳定的，其中$M$是正常波动的质量。两种理论中的特征值分布的行为也是不同的。我们还勾画了我们如何可以获得一个稳定的模糊四球${\bf S}^2_N\times{\bf S}^2_N$在大$N$限制的所有值的$M$以及模型的拓扑结构的变化，其中不同尺寸的领域之间的过渡观察。二维和四维的稳定模糊球精确地充当调节器，这是模糊几何和模糊物理的原始目标。简要讨论了这些空间上的模糊物理和模糊场论。

英文摘要：

A detailed Monte Carlo calculation of the phase diagram of bosonic IKKT Yang-Mills matrix models in three and six dimensions with quartic mass deformations is given. Background emergent fuzzy geometries in two and four dimensions are observed with a fluctuation given by a noncommutative $U(1)$ gauge theory very weakly coupled to normal scalar fields. The geometry, which is determined dynamically, is given by the fuzzy spheres ${\bf S}^2_N$ and ${\bf S}^2_N\times{\bf S}^2_N$ respectively. The three and six matrix models are in the same universality class with some differences. For example, in two dimensions the geometry is completely stable, whereas in four dimensions the geometry is stable only in the limit $M\longrightarrow \infty$, where $M$ is the mass of the normal fluctuations. The behavior of the eigenvalue distribution in the two theories is also different. We also sketch how we can obtain a stable fuzzy four-sphere ${\bf S}^2_N\times{\bf S}^2_N$ in the large $N$ limit for all values of $M$ as well as models of topology change in which the transition between spheres of different dimensions is observed. The stable fuzzy spheres in two and four dimensions act precisely as regulators which is the original goal of fuzzy geometry and fuzzy physics. Fuzzy physics and fuzzy field theory on these spaces are briefly discussed.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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