论文标题
两侧超尺度违反黑色麸皮的广义音量复杂性
Generalized Volume-Complexity For Two-Sided Hyperscaling Violating Black Branes
论文作者
论文摘要
在本文中，我们研究了$ d+2 $ dimensions中的两面未充电的HV黑色brane的广义音量 - 复杂性$ \ mathcal {c} _ {\ rm gen} $。最近在[Arxiv：2111.02429]中引入的该数量是复杂度=音量（CV）建议中体积的扩展，通过在量函数中添加较高的曲率校正，并添加较高的曲率校正。我们从数值计算$ \ MATHCAL {C} _ {\ rm gen} $的增长率，用于高标准违规指数$θ$和动态指数$ z $的不同值。据观察，$ \ Mathcal {C} _ {\ rm gen} $总是在较晚的时间线性增长，只要我们正确选择$λ$。此外，它从下面接近其迟到的时间值。对于$λ= 0 $的情况，我们找到了$θ$和$ z $的任意值的晚期增长率的分析表达式。但是，对于$λ\ neq 0 $，只能针对$θ$和$ z $的某些特定值进行分析计算。我们还研究了增长率对$ d $，$θ$，$ z $和$λ$的依赖性。此外，我们计算从体积复杂性获得的形成的复杂性，并表明它不是紫外线发散的。我们还检查了其对黑褐色的热熵和温度的依赖性。最后，对于较高的曲率校正是RICCI标量的线性组合，RICCI张量和Riemann张量的正方形的平方，我们还计算$ \ MATHCAL {C} _ {C} _ {\ rm gen} $的增长率。我们表明，对于耦合常数的适当值，较晚的时间增长率再次是线性的。
In this paper, we investigate generalized volume-complexity $\mathcal{C}_{\rm gen}$ for a two-sided uncharged HV black brane in $d+2$ dimensions. This quantity which was recently introduced in [arXiv:2111.02429], is an extension of volume in the Complexity=Volume (CV) proposal, by adding higher curvature corrections with a coupling constant $λ$ to the volume functional. We numerically calculate the growth rate of $\mathcal{C}_{\rm gen}$ for different values of the hyperscaling violation exponent $θ$ and dynamical exponent $z$. It is observed that $\mathcal{C}_{\rm gen}$ always grows linearly at late times provided that we choose $λ$ properly. Moreover, it approaches its late time value from below. For the case $λ=0$, we find an analytic expression for the late time growth rate for arbitrary values of $θ$ and $z$. However, for $λ\neq 0$, the late time growth rate can only be calculated analytically for some specific values of $θ$ and $z$. We also examine the dependence of the growth rate on $d$, $θ$, $z$ and $λ$. Furthermore, we calculate the complexity of formation obtained from volume-complexity and show that it is not UV divergent. We also examine its dependence on the thermal entropy and temperature of the black brane. At the end, we also numerically calculate the growth rate of $\mathcal{C}_{\rm gen}$ for the case where the higher curvature corrections are a linear combination of the Ricci scalar, square of the Ricci tensor and square of the Riemann tensor. We show that for appropriate values of the coupling constants, the late time growth rate is again linear.
