Time-dependent stabilization in AdS/CFT

  • Roberto Auzzi
  • Shmuel Elitzur
  • Sven Bjarke Gudnason
  • Eliezer Rabinovici
Article

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.

Keywords

AdS-CFT Correspondence Black Holes Spacetime Singularities 

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Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  • Roberto Auzzi
    • 1
  • Shmuel Elitzur
    • 1
  • Sven Bjarke Gudnason
    • 1
  • Eliezer Rabinovici
    • 1
  1. 1.Racah Institute of PhysicsThe Hebrew UniversityJerusalemIsrael

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