Department of Physics, Stanford University, Stanford, California 94305-4060, USA.
Phys Rev Lett. 2015 Sep 18;115(12):121602. doi: 10.1103/PhysRevLett.115.121602. Epub 2015 Sep 16.
To understand an emergent spacetime is to understand the emergence of locality. Entanglement entropy is a powerful diagnostic of locality, because locality leads to a large amount of short distance entanglement. Two-dimensional string theory is among the very simplest instances of an emergent spatial dimension. We compute the entanglement entropy in the large-N matrix quantum mechanics dual to two-dimensional string theory in the semiclassical limit of weak string coupling. We isolate a logarithmically large, but finite, contribution that corresponds to the short distance entanglement of the tachyon field in the emergent spacetime. From the spacetime point of view, the entanglement is regulated by a nonperturbative "graininess" of space.
要理解涌现的时空，就必须理解局域性的涌现。纠缠熵是局域性的有力诊断工具，因为局域性会导致大量短程纠缠。二维弦论是涌现空间维度的最简单实例之一。我们在弱弦耦合的半经典极限下计算了二维弦论对偶的大 N 矩阵量子力学的纠缠熵。我们分离出一个对数大但有限的贡献，它对应于涌现时空中类光场的短程纠缠。从时空的角度来看，纠缠是由空间的非微扰“颗粒度”来调节的。
