Entanglement entropy in three dimensional gravity
Entanglement entropy in three dimensional gravity
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DOI：
10.1007/jhep04(2015)031
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发表时间：
2014-12
影响因子：
5.4
通讯作者：
Henry Maxfield
中科院分区：
文献类型：
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作者：
Henry Maxfield
Ryu-Takayanagi(RT)和协变Hubeny-Rangamani-Takayanagi(HRT)建议将具有全息对偶的CFT中的纠缠熵与体几何中最小或极值表面的区域联系起来。我们展示了在三维纯重力中，如何通过将时空写成ADS 3的商来获得相关的调节测地线长度，从而将问题简化为简单的纯代数计算。我们解释了这是如何在洛伦兹和欧几里德的形式，然后说明它的使用，以获得一些新的结果在一些例子，包括旋转的BTZ，土豆，和几个虫洞几何。这包括单区间纠缠熵的空间和时间依赖性，尽管这些对称性只在事件视界之后被破坏。我们还讨论了在某些情况下允许从欧几里得计算的解析延拓得到HRT的考虑因素，以及相关的一类复杂的极值曲面。
The Ryu-Takayanagi (RT) and covariant Hubeny-Rangamani-Takayanagi (HRT) proposals relate entanglement entropy in CFTs with holographic duals to the areas of minimal or extremal surfaces in the bulk geometry. We show how, in three dimensional pure gravity, the relevant regulated geodesic lengths can be obtained by writing a spacetime as a quotient of AdS 3, with the problem reduced to a simple purely algebraic calculation. We explain how this works in both Lorentzian and Euclidean formalisms, before illustrating its use to obtain novel results in a number of examples, including rotating BTZ, thegeon, and several wormhole geometries. This includes spatial and temporal dependence of single-interval entanglement entropy, despite these symmetries being broken only behind an event horizon. We also discuss considerations allowing HRT to be derived from analytic continuation of Euclidean computations in certain contexts, and a related class of complexified extremal surfaces.