Phase transitions in 3D gravity and fractal dimension
Phase transitions in 3D gravity and fractal dimension
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DOI：
10.1007/jhep05(2018)080
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发表时间：
2018-02
影响因子：
5.4
通讯作者：
Xi Dong;S. Maguire;A. Maloney;Henry Maxfield
中科院分区：
文献类型：
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作者：
Xi Dong;S. Maguire;A. Maloney;Henry Maxfield
我们证明了对于具有更高亏格边界条件的三维引力场，如果理论具有足够轻的标量，则存在标量场凝聚的二阶相变。这种三维版本的全息超导相变发生，即使纯重力的解决方案是本地AdS 3。这是除了第一级Hawking-Page-like相变之间的不同的本地AdS 3 bodies。这意味着全息CFTs的Rényi熵将随着Rényi参数的变化而发生相变，只要理论具有比某个临界尺寸更轻的标量算子。我们表明，这个临界尺寸有一个优雅的数学解释为Hausdorff尺寸的限制集的商群AdS 3，并使用它来计算，分析模空间的边界附近和数值模空间的内部。我们比较这一CFT计算推广最近的工作贝林，凯勒和扎德，边界的临界尺寸使用更高的属共形块，并找到一个令人惊讶的良好匹配。
We show that for three dimensional gravity with higher genus boundary conditions, if the theory possesses a sufficiently light scalar, there is a second order phase transition where the scalar field condenses. This three dimensional version of the holographic superconducting phase transition occurs even though the pure gravity solutions are locally AdS 3. This is in addition to the first order Hawking-Page-like phase transitions between different locally AdS 3 handlebodies. This implies that the Rényi entropies of holographic CFTs will undergo phase transitions as the Rényi parameter is varied, as long as the theory possesses a scalar operator which is lighter than a certain critical dimension. We show that this critical dimension has an elegant mathematical interpretation as the Hausdorff dimension of the limit set of a quotient group of AdS 3, and use this to compute it, analytically near the boundary of moduli space and numerically in the interior of moduli space. We compare this to a CFT computation generalizing recent work of Belin, Keller and Zadeh, bounding the critical dimension using higher genus conformal blocks, and find a surprisingly good match.