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arXiv 2107.02178hep-th
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不求平均值的重力

Gravity without averaging

Andreas Blommaert, Jorrit Kruthoff

备注：
47 pages, 15 figures and many delta functions
发表信息：
SciPost Phys. 12, 073 (2022)
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摘要：

我们提出了一个引力理论，插值之间的JT重力，重力理论与固定边界的哈密顿量。为此，我们考虑一个矩阵积分与插入高斯方差$σ^2$，围绕矩阵$\textsf{H}_0$。收紧高斯使得矩阵积分不那么随机，并且最终它将系综折叠成一个哈密顿量$\textsf{H}_0$。这个模型提供了一个具体的设置来研究因式分解，以及系综中单个成员的引力对偶是什么。我们发现，随着$σ^2$的减小，JT引力子势得到修改，最终引力理论经历了一系列的相变，对应于超宏观空穴在时空中的增殖。此外，我们观察到，在Efetov模型的方法随机矩阵，非平均分解理论是由一个简单的鞍点。

英文摘要：

We present a gravitational theory that interpolates between JT gravity, and a gravity theory with a fixed boundary Hamiltonian. For this, we consider a matrix integral with the insertion of a Gaussian with variance $σ^2$, centered around a matrix $\textsf{H}_0$. Tightening the Gaussian renders the matrix integral less random, and ultimately it collapses the ensemble to one Hamiltonian $\textsf{H}_0$. This model provides a concrete setup to study factorization, and what the gravity dual of a single member of the ensemble is. We find that as $σ^2$ is decreased, the JT gravity dilaton potential gets modified, and ultimately the gravity theory goes through a series of phase transitions, corresponding to a proliferation of extra macroscopic holes in the spacetime. Furthermore, we observe that in the Efetov model approach to random matrices, the non-averaged factorizing theory is described by one simple saddle point.

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