发表机构
The Oskar Klein Centre and Department of Physics, Stockholm University; Science Institute, University of Iceland（斯德哥尔摩大学奥斯克·克莱因中心及物理系; 冰岛大学科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究三维BTZ黑洞中下落两点函数在奇点处的发散，发现其源于双扭曲算符交换，并指出包含哈格多恩增长的粒子塔会触发相变，使树级结果失效，修正区域与视界分离，符合黑洞互补性。
AI 中文摘要
在三维BTZ黑洞中，一个标量场的下落两点函数，其中一个算符插入外部区域，另一个沿类时测地线插入，当下落插入点到达黑洞奇点时发散。在边界描述中，这种发散完全来自双扭曲算符的交换，而非在多维情况下编码曲率奇点的多应力张量扇区。我们表明，包含具有哈格多恩增长的塔式大质量粒子会产生环修正，这些修正靠近奇点时变得重要，在那里触发哈格多恩相变，使得树级发散不可信。在边界理论中，相应的初级算符塔导致黑洞态中探针算符的广义自由场描述失效。在大黑洞中，这些修正仅在靠近奇点时变得重要，并在视界处保持指数抑制。因此，这些修正主导的区域与视界参数化分离，正如黑洞互补性原则所预期的那样。
英文摘要
An infalling two-point function of a scalar field in a three-dimensional BTZ black hole, with one operator inserted in the exterior and the other inserted along a timelike geodesic, diverges when the infalling insertion point reaches the black hole singularity. In the boundary description, this divergence is tied to the exchange of double-twist operators rather than to the multi-stress-tensor sector that encodes curvature singularities in higher dimensions. We show that the inclusion of a tower of massive particles with Hagedorn growth gives rise to loop corrections that become important near the singularity, where they trigger a Hagedorn transition that renders the tree-level divergence untrustworthy. In the boundary theory, the corresponding tower of primary operators leads to a breakdown of the generalized free field description of the probe operator in the black hole state. In a large black hole, these corrections become important only near the singularity and remain exponentially suppressed at the horizon. The region where these corrections dominate is therefore parametrically separated from the horizon, as anticipated by the principle of black hole complementarity.
Comments24 pages and 3 figures. v2 : Added references and clarified the boundary interpretation of the divergence
