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北美退伍军人节(Veterans Day),12 日无更新
arXiv 1605.08588hep-thgr-qc
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边界锥的重力场

Gravity duals of boundary cones

Joan Camps

摘要:

复制品技巧将Renyi熵定义为圆锥奇异几何上的配分函数。我们讨论他们的引力场:爱因斯坦方程在边界处诱导圆锥奇异度规的正则体解。当圆锥奇点支撑在平面或球面上时,这些解是双曲黑洞的改写。对于更一般的形状,这些解决方案是新的。我们构造他们的距离和强度的锥形奇点的双膨胀微扰,并提取真空极化由于锥。再现了Renyi熵对数发散结构的最新结果,特别是$f_b\neq f_c$ .我们详细讨论了动力学解决方案的奇异性的散装。这个决议是在协议与以前的建议,并表示一个非最小的解决“分裂问题”:一个明显的模糊性,在全息熵公式的某些理论与更高的衍生物。

英文摘要:

The replica trick defines Renyi entropies as partition functions on conically singular geometries. We discuss their gravity duals: regular bulk solutions to the Einstein equations inducing conically singular metrics at the boundary. When the conical singularity is supported on a flat or spherical surface, these solutions are rewritings of the hyperbolic black hole. For more general shapes, these solutions are new. We construct them perturbatively in a double expansion in the distance and strength of the conical singularity, and extract the vacuum polarisation due to the cone. Recent results about the structure of logarithmic divergences of Renyi entropies are reproduced ---in particular, $f_b\neq f_c$. We discuss in detail the dynamical resolution of the singularity in the bulk. This resolution is in agreement with a previous proposal, and indicates a non-minimal settling to the `splitting problem': an apparent ambiguity in the holographic entropy formula of certain theories with higher derivatives.

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