标题： 半经典稀疏子引力和非常钝的缺陷展开 显示英文标题

标题： Semi-classical dilaton gravity and the very blunt defect expansion

摘要： 我们研究在半经典极限下具有广义稀疏势的稀疏引力，既将其视为钝缺陷气体，也作为其自身的半经典理论。 我们将精确的缺陷气体图景与通过在测地线规范中天真地进行经典量子化得到的图景进行了比较。 我们发现由于测地线规范中的非微扰歧义性，经典方法中存在一个细微之处。 与JT引力不同，这种歧义性已经在圆盘层面出现。 这导致了一种与JT引力不同的机制，使得半经典近似在低温下失效。 在此过程中，我们提出新的、此前未被研究的鞍点对稀疏引力的状态密度有贡献。 这特别导致了对JT引力中圆盘层面状态密度的重新解释，即用两个具有固定能量边界条件的鞍点来解释：一个是在外视界处闭合的圆盘，另一个是次级复数鞍点，在内视界处闭合。 当使用缺陷展开来研究该理论时，我们展示了稀疏引力的平滑经典几何如何从$G_N \to 0$极限下的密集钝缺陷气体中产生。 经典鞍点来自于缺陷向负稀疏方向的吸引力与配置熵产生的统计压力之间的平衡。 最后，我们对由某些稀疏势描述的黑洞内部存在的类空奇点的性质进行了推测。 显示英文摘要

摘要： We explore dilaton gravity with general dilaton potentials in the semi-classical limit viewed both as a gas of blunt defects and also as a semi-classical theory in its own right. We compare the exact defect gas picture with that obtained by naively canonically quantizing the theory in geodesic gauge. We find a subtlety in the canonical approach due to a non-perturbative ambiguity in geodesic gauge. Unlike in JT gravity, this ambiguity arises already at the disk level. This leads to a distinct mechanism from that in JT gravity by which the semi-classical approximation breaks down at low temperatures. Along the way, we propose that new, previously un-studied saddles contribute to the density of states of dilaton gravity. This in particular leads to a re-interpretation of the disk-level density of states in JT gravity in terms of two saddles with fixed energy boundary conditions: the disk, which caps off on the outer horizon, and another, sub-leading complex saddle which caps off on the inner horizon. When the theory is studied using a defect expansion, we show how the smooth classical geometries of dilaton gravity arise from a dense gas of very blunt defects in the $G_N \to 0$ limit. The classical saddle points arise from a balance between the attractive force on the defects toward negative dilaton and a statistical pressure from the entropy of the configuration. We end with speculations on the nature of the space-like singularity present inside black holes described by certain dilaton potentials.