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arXiv · 1206.2902

Time-dependent stabilization in AdS/CFT

Roberto Auzzi·Shmuel Elitzur·Sven Bjarke Gudnason·Eliezer Rabinovici
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Abstract

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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Roberto Auzzi, Shmuel Elitzur, Sven Bjarke Gudnason, Eliezer Rabinovici. 2012-08-07. Time-dependent stabilization in AdS/CFT. https://doi.org/10.1007/jhep08(2012)035

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