发表机构
School of Physical Sciences, IIT Mandi（曼迪理工学院物理科学学院）
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AdS₃中共形耦合标量场HKLL重构问题的两种共形像，构建并求解平直空间受限镜问题，还通过共形映射观察smear函数的发散，为相关重构研究提供了新视角。
AI 中文摘要
我们研究了AdS₃中共形耦合标量场的HKLL重构问题的两种共形像。第一种映射是到爱因斯坦静态宇宙（ESU）一半区域上的狄利克雷问题，进一步的共形变换将该半ESU问题转化为(2+1)维平直空间中受匀加速圆形狄利克雷镜约束的无质量标量场问题。但对于全局HKLL问题，所得平直空间问题并非具有任意边界数据的一般局域镜问题，镜的响应数据必须属于从可归一化全局AdS模式继承而来的受限谱类。我们在平直空间中内在地构建并求解了该受限镜问题，在此过程中发现了一个本身不满足运动方程的有效 smear 函数示例。我们进一步考虑AdS-Rindler楔重构，通过共形映射到平直空间的合适坐标系，找到了一种简单方法来观察smear函数的发散。
英文摘要
We study two conformal images of the HKLL reconstruction problem for a conformally coupled scalar on AdS$_3$. The first mapping is to a Dirichlet problem on one half of the Einstein static universe. A further conformal transformation maps this half-ESU problem to a massless scalar in a region of $(2+1)$-dimensional Minkowski space bounded by an uniformly accelerated circular Dirichlet mirror. However, the global HKLL problem, the resulting flat-space problem is not a generic local mirror problem with arbitrary boundary data. Rather, the mirror response data must belong to a restricted spectral class inherited from normalizable global AdS modes. We formulate and solve this restricted mirror problem intrinsically in flat space. In the process, we find an example of a valid smearing function which itself does not satisfy the equations of motion. We further consider AdS-Rindler wedge reconstruction. By conformal mapping to an appropriate coordinate system in flat space, we find a simple way to see the blow-up of the smearing function.
CommentsCitation added. 21 pages, no figures
