标题： 带有新临界行为的修改后的c=1矩阵模型 显示英文标题

标题： A modified c=1 matrix model with new critical behavior

摘要： 通过在二维量子重力的$c=1$矩阵模型的作用量中引入一个$\int dt \, g\left(\Tr \Phi^2(t)\right)^2$项，我们发现随机曲面的新临界行为。 路径积分的平面极限生成多个球形“泡”，这些泡在单个点上相互接触。 在$g$的特殊值下，连通曲面的求和行为如$\Delta^2 \log\Delta$所示，其中$\Delta$是宇宙学常数 （面积为$A$的曲面求和行为如$A^{-3}$所示）。 为了比较，在传统的 $c=1$ 模型中，平面表面的求和行为如同 $\Delta^2/ \log\Delta$。 显示英文摘要

摘要： By introducing a $\int dt \, g\left(\Tr \Phi^2(t)\right)^2$ term into the action of the $c=1$ matrix model of two-dimensional quantum gravity, we find a new critical behavior for random surfaces. The planar limit of the path integral generates multiple spherical ``bubbles'' which touch one another at single points. At a special value of $g$, the sum over connected surfaces behaves as $\Delta^2 \log\Delta$, where $\Delta$ is the cosmological constant (the sum over surfaces of area $A$ goes as $A^{-3}$). For comparison, in the conventional $c=1$ model the sum over planar surfaces behaves as $\Delta^2/ \log\Delta$.