$M0$ -膜中泡利不相容原理的宇宙膨胀和收缩
Cosmological expansion and contraction from Pauli exclusion principle in $M0$-branes
摘要：
我们证明了泡利不相容原理在$M0$ -膜系统中可以引起位于$M3$ -膜上的宇宙的膨胀和收缩.我们从一个具有高对称性的$M0$ -膜系统开始，它们相互连接并形成成对的$M1$ -反$M1$ -膜。由此产生的对称性破缺产生了规范场，这些规范场存在于$M1$ -膜上，并扮演引力子张量模的角色，在$M1$和反$M1$膜之间产生吸引力。因此，存在于$M1$膜上的规范场和对称地附着在这些膜的所有部分上的标量场衰减为反对称地附着在膜的上下部分上的费米子，因此出现了泡利不相容原理。通过使$M1$ -膜相互闭合，平行自旋产生的曲率将不同于反平行自旋产生的曲率，这导致边界表面上的自由度数目与体区域中的自由度数目之间的不相等。这种行为在宇宙所处的$M3$ -膜中继承，因此这导致了宇宙膨胀和收缩的出现。在这个意义上，泡利不相容原理支配着宇宙动力学。
英文摘要：
We show that the Pauli exclusion principle in a system of $M0$-branes can give rise to the expansion and contraction of the universe which is located on an $M3$-brane. We start with a system of $M0$-branes with high symmetry, which join mutually and form pairs of $M1$-anti-$M1$-branes. The resulting symmetry breaking creates gauge fields that live on the $M1$-branes and play the role of graviton tensor modes, which induce an attractive force between the $M1$ and anti-$M1$ branes. Consequently, the gauge fields that live on the $M1$-branes, and the scalar fields which are attached symmetrically to all parts of these branes, decay to fermions that attach anti-symmetrically to the upper and lower parts of the branes, and hence the Pauli exclusion principle emerges. By closing $M1$-branes mutually, the curvatures produced by parallel spins will be different from the curvatures produced by anti-parallel spins, and this leads to an inequality between the number of degrees of freedom on the boundary surface and the number of degrees of freedom in the bulk region. This behavior is inherited in the $M3$-brane on which the universe is located, and hence this leads to the emergence of the universe expansion and contraction. In this sense, the Pauli exclusion principle rules the cosmic dynamics.
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