二维和三维中的有限因果集量子引力
Dimensionally Restricted Causal Set Quantum Gravity: Examples in Two and Three Dimensions
摘要：
研究了具有非平凡整体拓扑的$2$和$3$时空维中的维数限制的非微扰因果集量子动力学.因果集样本空间是从因果嵌入到时空格中生成的，时空格分别具有$2$和$3$维度的全局空间拓扑$S^1$和$T^2$。在解析延拓后，利用马尔可夫链蒙特卡罗（MCMC）模拟方法研究了这些样本空间上的量子引力配分函数。在$2$和$3$两个维度中，我们发现了一个相变，它将作用的主导性与熵的主导性分开。行动主导阶段的特点是“分层”的偏序集具有高度的连通性，而在熵主导阶段的因果集是流形。这种相变的性质类似于$2$阶的样本空间，这是拓扑平凡的，因此表明这是一个通用的功能，尺寸限制的样本空间。模拟使用一个新开发的框架因果集MCMC计算。我们的是第一次实现的因果集动力学限制在$3$维。
英文摘要：
We study dimensionally restricted non-perturbative causal set quantum dynamics in $2$ and $3$ spacetime dimensions with non-trivial global spatial topology. The causal set sample space is generated from causal embeddings into spacetime lattices with global spatial topology $S^1$ and $T^2$ in $2$ and $3$ dimensions, respectively. The quantum gravity partition function over these sample spaces is studied using Markov Chain Monte Carlo (MCMC) simulations after analytic continuation. In both $2$ and $3$ dimensions we find a phase transition that separates the dominance of the action from that of the entropy. The action dominated phase is characterised by ``layered'' posets with a high degree of connectivity, while the causal sets in the entropy dominated phase are manifold-like. This phase transition is similar in character to that seen for the sample space of $2$-orders, which are topologically trivial, hence suggesting that this is a generic feature of dimensionally restricted sample spaces. The simulations use a newly developed framework for causal set MCMC calculations. Ours is the first implementation of a causal set dynamics restricted to $3$ dimensions.
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