论文标题
ADS/CFT中平均的精确测试
A precision test of averaging in AdS/CFT
论文作者
论文摘要
我们重新考虑虫洞在AD/CFT对应中的作用。我们专注于将两个渐近广告或双曲线区域与$ \ mathbb {s}^1 \ times \ mathbb {s}^{d-1} $ bouncy连接两个渐近广告或双曲线区域。对于爱因斯坦的方程式没有解决方案，因为虫洞具有延伸到无穷大的模量。要查找壳虫孔，我们必须稳定这种模量，我们可以通过在两个边界上固定总能量来做到这一点。这样的虫洞将鞍点近似与量子重力中的非标准问题相近似，在那里我们固定两个渐近边界并限制了共同的能量。至关重要的是，即使由于固定能量限制，双重数量也不会分解为单个CFT。从这个数量中，我们提取了微型频谱形式的涂片版本。对于混乱的理论，该数量是自动平均的，即通过在能量窗口上平均或耦合常数来及时及时征用。 我们继续进行精确测试，其中涉及微型频谱形式，其中两个副本的耦合常数略有不同。在混乱的理论中，该形式以普遍预测的一个复制物理学的速度平稳衰减，前提是在窗口上或耦合上有平均值。我们计算全息理论的预期衰减率，以及来自虫洞的外形，两者完全同意广泛的ADS中的两种两衍生有效的现场理论。这给出了ADS/CFT中平均值的精确测试。 我们的结果解释了许多关于虫洞和AD中分解的令人困惑的事实，并建议我们应该将重力有效的野外理论视为介质描述，类似于量子混乱系统的半经典介绍性描述。
We reconsider the role of wormholes in the AdS/CFT correspondence. We focus on Euclidean wormholes that connect two asymptotically AdS or hyperbolic regions with $\mathbb{S}^1\times \mathbb{S}^{d-1}$ boundary. There is no solution to Einstein's equations of this sort, as the wormholes possess a modulus that runs to infinity. To find on-shell wormholes we must stabilize this modulus, which we can do by fixing the total energy on the two boundaries. Such a wormhole gives the saddle point approximation to a non-standard problem in quantum gravity, where we fix two asymptotic boundaries and constrain the common energy. Crucially the dual quantity does not factorize even when the bulk is dual to a single CFT, on account of the fixed energy constraint. From this quantity we extract a smeared version of the microcanonical spectral form factor. For a chaotic theory this quantity is self-averaging, i.e. well-approximated by averaging over energy windows, or over coupling constants. We go on to give a precision test involving the microcanonical spectral form factor where the two replicas have slightly different coupling constants. In chaotic theories this form factor is known to smoothly decay at a rate universally predicted in terms of one replica physics, provided that there is an average either over a window or over couplings. We compute the expected decay rate for holographic theories, and the form factor from a wormhole, and the two exactly agree for a wide range of two-derivative effective field theories in AdS. This gives a precision test of averaging in AdS/CFT. Our results interpret a number of confusing facts about wormholes and factorization in AdS and suggest that we should regard gravitational effective field theory as a mesoscopic description, analogous to semiclassical mesoscopic descriptions of quantum chaotic systems.
