关于来自近视界共形场论的 't Hooft 激波对易子的注记
Note on 't Hooft's Shock Wave Commutators From Near Horizon Conformal Field Theory
AI总结：
本文基于因果菱形中量子自由度服从1+1维截断共形场论的假设，构建了 't Hooft 激波对易关系的有限模型，通过动量与Dirac本征值截断消除了重合点发散。
摘要：
我们基于以下假设构建了 't Hooft 激波对易关系的一个有限模型：在爱因斯坦方程解的因果菱形中的量子自由度，是一个（截断的）1+1 维共形场论（CFT）的自由度，其中心荷通过将 Cardy 公式与广义 Bekenstein-Hawking 公式相等而与该菱形全息屏的面积相关。该特定的 CFT 是自由无质量费米子的一个精确边缘微扰，这是受全息时空（HST）计划的启发。1+1 维中的动量截断以及横向几何上的 Dirac 本征值截断，在菱形面积有限时修改了 't Hooft 关系，并消除了由这些对易关系导出的预测中的所有重合点发散。
英文摘要：
We construct a finite model of 't Hooft's shock wave commutation relations from the ansatz\cite{Carlip}\cite{Solodukhin}\cite{BZ} that the quantum degrees of freedom in a causal diamond in a solution of Einstein's Equations are those of a (cut-off\cite{BZ}\cite{hilbertbundles} ) 1 + 1 dimensional conformal field theory (CFT) with central charge related to the area of the diamond's holographic screen by equating Cardy's formula with the generalized Bekenstein-Hawking formula\cite{ted95}\cite{fsb}. The particular CFT is an exactly marginal perturbation of free massless fermions, as motivated by the Holographic Space-Time\cite{hilbertbundles} (HST) program. The momentum cutoff in $1 + 1$ dimensions and the Dirac eigenvalue cutoff on the transverse geometry, modify the 't Hooft relations when the area of the diamond is finite and remove all coincident point divergences in predictions derived from these commutation relations.
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