微扰论的连续有效性扩展：AdS稳定岛的持久性
Conditionally Extended Validity of Perturbation Theory: Persistence of AdS Stability Islands
摘要：
用截断的微扰展开近似非线性动力学可能在一段时间内是准确的，但它通常在很长的时间尺度上是一个小的展开参数。有一些有趣的情况下，这种崩溃并没有发生。我们提供了一个数学上的一般和精确的定义，这些场合，我们证明了截断理论的有效性平凡地延伸到长时间尺度。这使我们能够利用数值结果，这是只能在有限的时间内，合理地预测动态时，扩展参数为零，因此长的时间尺度走向无穷大。特别是，这表明AdS（in）稳定性问题中现有的非崩溃解持续到零振幅极限，与Dias，Horowitz，Marolf和Santos预测收缩到测量零的猜想相反[1]。我们还指出了为什么坍缩解的持久性更难证明，以及Bizon，Maliborski和Rostoworowski最近的有趣进展是如何尚未存在的。
英文摘要：
Approximating nonlinear dynamics with a truncated perturbative expan- sion may be accurate for a while, but it in general breaks down at a long time scale that is one over the small expansion parameter. There are interesting occasions in which such breakdown does not happen. We provide a mathematically general and precise definition of those occasions, in which we prove that the validity of truncated theory trivially extends to the long time scale. This enables us to utilize numerical results, which are only obtainable within finite times, to legitimately predict the dynamic when the expansion parameter goes to zero, thus the long time scale goes to infinity. In particular, this shows that existing non-collapsing solutions in the AdS (in)stability problem persist to the zero-amplitude limit, opposing the conjecture by Dias, Horowitz, Marolf and Santos that predicts a shrinkage to measure-zero [1]. We also point out why the persistence of collapsing solutions is harder to prove, and how the recent interesting progress by Bizon, Maliborski and Rostoworowski is not there yet [2].
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