标题： 二维引力模型与无质量标量场耦合时的伪拓扑转变 显示英文标题

标题： Pseudo-topological transitions in 2D gravity models coupled to massless scalar fields

摘要： 我们研究了由二维因果动力学三角化（CDT）耦合到$d$无质量标量场所生成的几何结构。使用类似于研究四维CDT的方法，我们证明存在一个$c=1$“障碍”，类似于在非临界弦理论中遇到的$c=1$障碍，但CDT相变更容易被数值检测到。对于$d\leq 1$，我们观察到时间平移不变性以及完全由手征均匀环面拓扑结构周围的量子涨落支配的几何结构。对于$d>1$，有效平均几何结构不再是环面而是“半经典”的且球形的，Hausdorff维度为$d_H = 3$。在$d>1$部分，我们研究了半经典空间体积分布的时间依赖性，并表明观察到的行为可以用有效的mini-超空间作用量来描述，这与在三维和四维纯CDT模拟的de Sitter相以及三维CDT-like Hořava-Lifshitz模型中发现的作用量类似。 显示英文摘要

摘要： We study the geometries generated by two-dimensional causal dynamical triangulations (CDT) coupled to $d$ massless scalar fields. Using methods similar to those used to study four-dimensional CDT we show that there exists a $c=1$ "barrier", analogous to the $c=1$ barrier encountered in non-critical string theory, only the CDT transition is easier to be detected numerically. For $d\leq 1$ we observe time-translation invariance and geometries entirely governed by quantum fluctuations around the uniform toroidal topology put in by hand. For $d>1$ the effective average geometry is no longer toroidal but "semiclassical" and spherical with Hausdorff dimension $d_H = 3$. In the $d>1$ sector we study the time dependence of the semiclassical spatial volume distribution and show that the observed behavior is described an effective mini-superspace action analogous to the actions found in the de Sitter phase of three- and four-dimensional pure CDT simulations and in the three-dimensional CDT-like Ho\v{r}ava-Lifshitz models.