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arXiv 1206.2902hep-th
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AdS/CFT系统的时变镇定

Time-dependent stabilization in AdS/CFT

Roberto Auzzi, Shmuel Elitzur, Sven Bjarke Gudnason, Eliezer Rabinovici

备注：
LaTeX, 38 pages, 13 figures. V2: appendix C added, references added and typos corrected
发表信息：
JHEP 1208:035,2012
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摘要：

我们考虑的理论与时间相关的哈密顿交替之间的有界和无界从下面。对于适当的频率，可以发生动态稳定，从而使系统的有效势稳定。我们首先研究了一个自由场论与时间相关的质量项的环面，发现的稳定区域描述的马蒂厄方程的相图。使用数论，我们已经找到了一个紧致化方案，如以避免共振的所有动量模式的理论。我们进一步考虑了三维时空中球体上的共形场论的引力对偶，它被双迹算子变形。重力对偶的理论与一个常数无界的潜力发展大紧缩奇点，我们研究当这样的奇点可以治愈的动力稳定。我们数值求解爱因斯坦标量运动方程的情况下，时间依赖的双轨迹变形，并发现，足够高的频率的理论是动态稳定的和大的紧缩得到屏蔽的黑洞地平线。

英文摘要：

We consider theories with time-dependent Hamiltonians which alternate between being bounded and unbounded from below. For appropriate frequencies dynamical stabilization can occur rendering the effective potential of the system stable. We first study a free field theory on a torus with a time-dependent mass term, finding that the stability regions are described in terms of the phase diagram of the Mathieu equation. Using number theory we have found a compactification scheme such as to avoid resonances for all momentum modes in the theory. We further consider the gravity dual of a conformal field theory on a sphere in three spacetime dimensions, deformed by a doubletrace operator. The gravity dual of the theory with a constant unbounded potential develops big crunch singularities; we study when such singularities can be cured by dynamical stabilization. We numerically solve the Einstein-scalar equations of motion in the case of a time-dependent doubletrace deformation and find that for sufficiently high frequencies the theory is dynamically stabilized and big crunches get screened by black hole horizons.

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