论文标题
扭曲的保形场理论的复杂性
Complexity of warped conformal field theory
论文作者
论文摘要
在二维中，扭曲的形成性野外理论是异国情调的非局部，洛伦兹违反了以Virasoro-kac-moody对称为特征的野外理论，并吸引了很多关注，因为候选人的边界双重偶数$ _3 $ spacetime，从而扩大了渐近的广告范围。在这里，我们使用\ emph {电路复杂性}来调查wcft $ _2 $ \，s作为工具。首先，我们计算显示线性紫外线发散结构的全息体积复杂性（CV），更类似于本地CFT $ _2 $，并且对Virasoro Central Chentral Charter $ C $和$ U（1）$ KAC-MOODY级别$ k $ k $具有非常复杂的依赖性。接下来，我们考虑基于virasoro-kac-moody对称门的电路复杂性，其中复杂性函数是对Virasoro-kac-moody组的共同连接轨道的几何作用（组）作用。我们考虑了一种特殊的解决方案，以使复杂性与``时间''线性缩放。在半经典限制中（大$ C，K $，而$ C/K $保持有限且较小），全息体积复杂性和电路复杂性都用$ K $线性地缩放。
Warped conformal field theories in two dimensions are exotic nonlocal, Lorentz violating field theories characterized by Virasoro-Kac-Moody symmetries and have attracted a lot of attention as candidate boundary duals to warped AdS$_3$ spacetimes, thereby expanding the scope of holography beyond asymptotically AdS spacetimes. Here we investigate WCFT$_2$\,s using \emph{circuit complexity} as a tool. First we compute the holographic volume complexity (CV) which displays a linear UV divergence structure, more akin to that of a local CFT$_2$ and has a very complicated dependence on the Virasoro central charge $c$ and the $U(1)$ Kac-Moody level parameter $k$. Next we consider circuit complexity based on Virasoro-Kac-Moody symmetry gates where the complexity functional is the geometric (group) action on coadjoint orbits of the Virasoro-Kac-Moody group. We consider a special solution to extremization equations for which complexity scales linearly with ``time''. In the semiclassical limit (large $c,k$, while $c/k$ remains finite and small) both the holographic volume complexity and circuit complexity scales linearly with $k$.
