TY - JOUR
T1 - Time-dependent stabilization in AdS/CFT
AU - Auzzi, Roberto
AU - Elitzur, Shmuel
AU - Gudnason, Sven Bjarke
AU - Rabinovici, Eliezer
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
KW - AdS-CFT Correspondence
KW - Black Holes
KW - Spacetime Singularities
UR - http://www.scopus.com/inward/record.url?scp=84865260865&partnerID=8YFLogxK
U2 - 10.1007/JHEP08(2012)035
DO - 10.1007/JHEP08(2012)035
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AN - SCOPUS:84865260865
SN - 1126-6708
VL - 2012
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
IS - 8
M1 - 35
ER -