AI 中文总结
研究体对偶为洛夫洛克引力的全息共形场论中的类时纠缠第一定律，通过双维克旋转公式和雅各布森 - 迈尔斯熵泛函计算线性变化，发现其与洛夫洛克引力线性化场方程在特定区域内等价。
AI 中文摘要
我们研究了体对偶为洛夫洛克引力的全息共形场论中的类时纠缠第一定律。利用类时纠缠熵的双维克旋转公式以及雅各布森 - 迈尔斯熵泛函，我们计算了双曲子区域的全息类时纠缠熵的线性变化。对于立方洛夫洛克引力，我们明确表明，一个单一的通用乘法重整化因子决定了高曲率相互作用如何进入熵和模块化哈密顿量的变化中，对于低能热激发导致\(\Delta S = \Delta\langle H\rangle\)。然后我们将分析扩展到在费弗曼 - 格雷厄姆规范下围绕反德西特时空的任意阶洛夫洛克引力。对于可归一化微扰，雅各布森 - 迈尔斯泛函的变化简化为爱因斯坦引力的结果乘以在洛夫洛克引力的线性化场方程中重整化有效牛顿常数的相同耦合依赖因子。我们进一步表明，对于所考虑的微扰类，在共形极限下边界贡献消失。因此，在本文所考虑的双曲和微扰区域内，类时纠缠第一定律等同于关于最大对称背景的洛夫洛克引力的线性化场方程。
英文摘要
We investigate the timelike entanglement first law in holographic conformal field theories whose bulk dual is Lovelock gravity. Using the double Wick rotation formulation of timelike entanglement entropy together with the Jacobson-Myers entropy functional, we compute the linear variation of holographic timelike entanglement entropy for hyperbolic subregions. For cubic Lovelock gravity, we explicitly show that a single, universal multiplicative renormalization factor governs how higher curvature interactions enter the variations of both the entropy and the modular Hamiltonian, leading to $ΔS=Δ\langle H\rangle$ for low-energy thermal excitations. We then extend the analysis to Lovelock gravity of arbitrary order around the anti-de Sitter spacetime in the Fefferman-Graham gauge. For normalizable perturbations, the variation of the Jacobson-Myers functional reduces to the Einstein gravity's result multiplied by the same coupling-dependent factor that renormalizes the effective Newtonian constant in the linearized field equations of Lovelock gravity. We further show that the boundary contribution vanishes in the conformal limit for the class of perturbations considered. Consequently, the timelike entanglement first law is equivalent to the linearized field equations of Lovelock gravity about the maximally symmetric background, within the hyperbolic and perturbative regime considered in the present paper.
Comments41 pages; citations added
