论文标题
森林中的流动
A Flow in the Forest
论文作者
论文摘要
使用矩阵 - 孔定理和Parisi-Sourlas Trick，我们制定并求解具有非多功能电势的一个Matrix模型，该模型为动态平面图提供了扰动理论，可为大量的无旋转费用。这是2D量子重力的晶格版本，与巨大的无旋转费用相连。我们的模型等效地描述了同一图上跨越森林的合奏。该溶液是根据椭圆曲线配制的。然后，当森林中的图形和树木在宏观上较大时，我们将重点关注近乎临界的缩放限制。在此限制中，我们获得了通用的单点缩放函数（冷凝水），并根据兰伯特函数进行参数化。我们的结果提供了一个罕见的例子，可以在其中探索两个重力模型之间的流动 - 在这种情况下，与C = -2（大树木制度）和C = 0（小树机制）相结合的共形物质理论。我们还以相同的临界极限计算了Dirichlet和Neumann边界条件的圆盘分区功能。
Using the matrix-forest theorem and the Parisi-Sourlas trick we formulate and solve a one-matrix model with non-polynomial potential which provides perturbation theory for massive spinless fermions on dynamical planar graphs. This is a lattice version of 2d quantum gravity coupled to massive spinless fermions. Our model equivalently describes the ensemble of spanning forests on the same graphs. The solution is formulated in terms of an elliptic curve. We then focus on a near-critical scaling limit when both the graphs and the trees in the forests are macroscopically large. In this limit we obtain universal one-point scaling functions (condensates), parameterized in terms of the Lambert function. Our results provide a rare example where one can explore the flow between two gravity models -- in this case, the theories of conformal matter coupled to 2d gravity with c=-2 (large trees regime) and c=0 (small trees regime). We also compute the disc partition functions with Dirichlet and Neumann boundary conditions in the same critical limit.
