类光延迟关联函数与视界
Light-like retarded correlators and the horizon
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- Indian Institute of Science（印度科学学院）
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中文总结 AI 辅助
研究共形场论中类光延迟关联函数在有限温度下大动量时的反常标度，利用$AdS/CFT$，通过二维精确结果、数值分析及WKB近似确定不同视界黑洞的标度行为，还评估了应力张量关联函数的反常标度指数。
中文摘要 AI 辅助
我们表明，在有限温度下使用$AdS/CFT$对标量原初算符的共形场论中的延迟关联函数，在大的类光动量下反常标度。反常标度取决于视界的曲率。将动量设为频率$\omega$，具有平面视界的黑洞的延迟关联函数标度为$\omega^{\frac{2}{d + 2}(2\Delta - d)}$，与一般固定动量和大频率下量纲分析预期的$\omega^{2\Delta - d}$标度行为不同。$\Delta$是原初的维度，$d$是时空维度。对于具有球形和双曲视界的黑洞，当频率平方等于沿视界的卡西米尔量时，延迟关联函数标度为$\omega^{\frac{2\Delta - d}{2}}$。我们通过二维的精确结果、对$AdS_5$平面黑洞的许恩方程的数值分析以及一般$d$下的WKB近似来确定这一点。双曲视界黑洞的精确结果以及大$d$时的分析为反常标度行为提供了额外检验。最后我们评估了应力张量关联函数在所有三个通道中的反常标度指数。
英文摘要
We show that retarded correlators in conformal field theories of scalar primary operators evaluated at finite temperature using $AdS/CFT$ scale anomalously at large light like momenta. The anomalous scaling depends on the curvature of the horizon. Setting the momenta equal to the frequency $ω$, the retarded correlator for black holes with planar horizons scales as $ω^{\frac{2}{d+2} (2Δ- d) }$ as opposed to the scaling behaviour of $ω^{2Δ- d}$ expected by dimensional analysis at generic fixed momenta and large frequencies. $Δ$ is the dimension of the primary and $d$, the number of space-time dimensions. For black holes with spherical and hyperbolic horizons when the frequency squared equals the Casimir along the horizon, the retarded correlator scales as $ω^{\frac{2Δ-d}{2} }$. We establish this using exact results in $d=2$, and a numerical analysis of the Heun equation for the $AdS_5$ planar black hole and finally using the WKB approximation in general $d$. The exact result for black holes with hyperbolic horizon as well as the analysis at large $d$ provides additional checks for the anomalous scaling behaviour. Finally we evaluate the anomalous scaling exponent for the stress tensor correlator in all its 3 channels.
