标题： 具有新的临界行为的修正的 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： 通过在二维量子引力的$\int dt \, g\left(\Tr \Phi^2(t)\right)^2$矩阵模型的作用量中引入一个$c=1$项，我们发现了随机表面的一种新临界行为。 路径积分的平面极限生成多个球形“气泡”，这些气泡在单个点处相互接触。 当$g$取特殊值时，关于连接表面的求和行为表现为$\Delta^2 \log\Delta$，其中$\Delta$是宇宙学常数（面积为$A$的表面求和行为表现为$A^{-3}$）。 为了比较，在常规的$c=1$模型中，平面表面的求和行为表现为$\Delta^2/ \log\Delta$。 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 $\Delta^2/ \log\Delta$.