论文标题
扫描时空与纠缠模式
Scanning space-time with patterns of entanglement
论文作者
论文摘要
在$ {\ rm ads} _3/{\ rm cft} _2 $设置中，我们阐明了如何通过$ a_ {n-3} $ n \ n \ geq 4 $ geq 4 $ clge e e gequlbra的$ a_ {n-3} $ a_ {n-3} $ a_ {n-3} $ a_ {n-3} $ a_ {在静态情况下，这种编码的动力在运动空间中表现出来，这是de sitter空间的副本$ {\ rm ds} _2 $，以特别有启发性的方式。对于将边界分配到$ n $区域的分区，与重叠区域的有条件相互信息相关的纠缠模式与大地测量$ n $ gons的三角剖分有关。然后将这种三角剖分映射到运动学空间中的因果模式。对于固定的$ n $，所有因果模式的空间都与AssociaHedron $ {\ Mathcal K}^{n-3} $相关的一个对象。在这一因果模式的空间上，群集动力学由Zamolodchikov的$ y $ $ $ $ - $（a_ {n-3}，a_1）$提供的递归作用。我们观察到因果模式的空间配备了部分秩序，并且与塔玛里晶格是同构的。因果模式的突变可以通过在过去的光锥中以$ {\ rm ds} _2 $相互作用的$ n-3 $粒子的步行封装。
In the ${\rm AdS}_3/{\rm CFT}_2$ setup we elucidate how gauge invariant boundary patterns of entanglement of the CFT vacuum are encoded into the bulk via the coefficient dynamics of an $A_{N-3}$, $N\geq 4$ cluster algebra. In the static case this dynamics of encoding manifests itself in kinematic space, which is a copy of de Sitter space ${\rm dS}_2$, in a particularly instructive manner. For a choice of partition of the boundary into $N$ regions the patterns of entanglement, associated with conditional mutual informations of overlapping regions, are related to triangulations of geodesic $N$-gons. Such triangulations are then mapped to causal patterns in kinematic space. For a fixed $N$ the space of all causal patterns is related to the associahedron ${\mathcal K}^{N-3}$ an object well-known from previous studies on scattering amplitudes. On this space of causal patterns cluster dynamics acts by a recursion provided by a Zamolodchikov's $Y$-system of type $(A_{N-3},A_1)$. We observe that the space of causal patterns is equipped with a partial order, and is isomorphic to the Tamari lattice. The mutation of causal patterns can be encapsulated by a walk of $N-3$ particles interacting in a peculiar manner in the past light cone of a point of ${\rm dS}_2$.
