复杂性和大容量，一个纽约时报的故事
Complexity and the bulk volume, a new York time story
摘要：
我们研究的边界描述的体积最大柯西切片使用最近推导出的体积和边界辛形式之间的等价性。已知常平均曲率切片的体积与“约克时间”正则共轭。我们用它来构造边界变形，这是共轭的体积在少数的例子，如空的AdS，一个backreacting标量凝聚，或在无限时间的热场双。我们提出了一个可能的自然边界解释这种变形，并使用它来激发一个具体的版本的复杂性=体积猜想，其中边界复杂性被定义为能量的测地线在凯勒几何的半边源。我们检查这个猜想的巴尼亚多斯几何和一个迷你超空间版本的热场双态。最后，我们证明了边缘标量的量子信息度规的精确对偶是由一个特别简单的辛通量给出的，而不是以前所描述的体积。
英文摘要：
We study the boundary description of the volume of maximal Cauchy slices using the recently derived equivalence between bulk and boundary symplectic forms. The volume of constant mean curvature slices is known to be canonically conjugate to "York time". We use this to construct the boundary deformation that is conjugate to the volume in a handful of examples, such as empty AdS, a backreacting scalar condensate, or the thermofield double at infinite time. We propose a possible natural boundary interpretation for this deformation and use it to motivate a concrete version of the complexity=volume conjecture, where the boundary complexity is defined as the energy of geodesics in the Kähler geometry of half sided sources. We check this conjecture for Bañados geometries and a mini-superspace version of the thermofield double state. Finally, we show that the precise dual of the quantum information metric for marginal scalars is given by a particularly simple symplectic flux, instead of the volume as previously conjectured.
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