Topological Complexity in AdS3/CFT2
Topological Complexity in AdS3/CFT2
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DOI：
10.1002/prop.201800034
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发表时间：
2017-10
期刊：
影响因子：
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通讯作者：
Raimond Abt;J. Erdmenger;H. Hinrichsen;C. Melby-Thompson;R. Meyer;C. Northe;Ignacio A. Reyes
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文献类型：
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作者：
Raimond Abt;J. Erdmenger;H. Hinrichsen;C. Melby-Thompson;R. Meyer;C. Northe;Ignacio A. Reyes
我们在ADS3/CFT2对应中考虑了次区域复杂性。我们改写了体积方案，根据该方案，约化密度矩阵的复杂性由包含在相关Ryu-Takayanagi(RT)曲面内的时空体积通过曲率上的积分给出。利用Gauss-Bonnet定理，我们计算了一般纠缠区和温度下的这个量。特别是，我们发现，在RT表面变化下出现的不连续是由固定的拓扑贡献给出的，与纠缠区的温度或细节无关。我们给出了张量网络背景下的分区复杂性的定义和解释，并用数值方法证明了它利用其与伊辛模型的关系再现了随机张量网络情况下全息计算的定性特征。最后，我们给出了在CFT中使用运动学空间形式直接计算分区复杂性的规定，并用它复制了我们在零温下得到的一些显式重力结果。因此，我们得到了重力网络和张量网络方法之间对子区域复杂性的具体匹配结果，以及CFT规定。
We consider subregion complexity within the AdS3/CFT2 correspondence. We rewrite the volume proposal, according to which the complexity of a reduced density matrix is given by the spacetime volume contained inside the associated Ryu‐Takayanagi (RT) surface, in terms of an integral over the curvature. Using the Gauss‐Bonnet theorem we evaluate this quantity for general entangling regions and temperature. In particular, we find that the discontinuity that occurs under a change in the RT surface is given by a fixed topological contribution, independent of the temperature or details of the entangling region. We offer a definition and interpretation of subregion complexity in the context of tensor networks, and show numerically that it reproduces the qualitative features of the holographic computation in the case of a random tensor network using its relation to the Ising model. Finally, we give a prescription for computing subregion complexity directly in CFT using the kinematic space formalism, and use it to reproduce some of our explicit gravity results obtained at zero temperature. We thus obtain a concrete matching of results for subregion complexity between the gravity and tensor network approaches, as well as a CFT prescription.