标题： 闭合$\mathbf{dS_{2} }$时空的双重全息模型中的相变 显示英文标题

标题： Phase transition in a doubly holographic model of closed $\mathbf{dS_{2} }$ spacetime

摘要： 双全息性已被证明是理解时空纠缠的强大方法。 在本文中，我们研究了${\mathrm{dS_{2}} }$时空中的双重全息构造。 我们发现在这个模型中除了 Hartman-Maldacena 表面和岛屿表面之外，还存在一个新的极值表面，这可能导致更复杂的相结构。 我们然后提出了一种广义的互熵来解释相变。 然而，这个极值表面有一个微妙的特性，即当这个鞍点占主导地位时，测地线的一部分长度为负。 这是因为测地线的负部分位于体几何的视界之内。 我们转向${\mathrm{AdS_{2}} }$时空，并发现这种微妙性仍然存在。 我们提出一个简单的解决方案来解决这个问题。 显示英文摘要

摘要： Double holography has been proved to be a powerful method in comprehending the spacetime entanglement. In this paper we investigate the doubly holographic construction in ${\mathrm{dS_{2}} }$ spacetime. We find that in this model there exists a new extremal surface besides the Hartman-Maldacena surface and the island surface, which could lead to a more complex phase structure. We then propose a generalized mutual entropy to interpret the phase transition. However, this extremal surface has a subtle property that the length of a part of the geodesic is negative when this saddle is dominant. This is because the negative part of the geodesic is within the horizon of the bulk geometry. We move to the ${\mathrm{AdS_{2}} }$ spacetime and find this subtlety still exists. We purpose a simple solution to this issue.