(In)Stabilities and Complementarity in AdS/CFT
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(In)Stabilities and Complementarity in
AdS/CFT
Eliezer RabinoviciThe Hebrew University, Jerusalem
Based on works with J.L.F Barbon Based on work with R. Auzzi, S. Elitzur and
S.B. Gudnason
Strings 2012 Munich July
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• J. L. F. Barbon and E. Rabinovici, “AdS Crunches, CFT Falls And Cosmological Complementarity,” JHEP 1104, 044 (2011) [arXiv:1102.3015 [hep-th]].
• J. L. F. Barbon and E. Rabinovici, “Holography of AdS vacuum bubbles,”JHEP 1004, 123 (2010) [arXiv:1003.4966 [hep-th]].
• J. L .F. Barbon and E. Rabinovici, work in progress.
• R. Auzzi, S. Elitzur, S. B. Gudnason and E. Rabinovici, “Time-dependent stabilization in AdS/CFT,”Accepted for publication in JHEP [arXiv:1206.2902 [hep-th]].
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References
• S. R. Coleman , F. De Luccia
• T. Banks
• T. Hertog , G. T. Horowitz, B. Craps, N. Turok, A. Bernamonti
• S. Elitzur, A. Giveon, M. Porrati , E. Rabinovici
• S. de Haro, I. Papadimitriou , A. C. Petkou
• J. Orgera, J. Polchinski,; D. Harlow
• J. Maldacena
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Content
• Introduction
• Bulk
• AdS set up
• Boundary
• Complementarity
• Butterflies
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Dualities
• Geometry
• Topology
• Number of dimensions, small and large
• (non-)Commutativity
• Singularity structure
• Associativity
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=
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• Singularities express a breakdown of our knowledge/approximations
• In general-covariantly invariant theories, singularities can hide behind horizons
• Finite black hole entropy can be reconstructed from the outside
• Can infinite entropy of a crunch be reconstructed as well?
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Ads set up
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In AdS what you see is not what you get
?
• In AdS volume scales like area for large enough Area. The unstable state can be stable or:
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boundary
Non perturbative definition of the theory.
There are several possible QFT duals on the bondary
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• If the boundary theory is well defined so is the crunch in the bulk.
• For the bulk crunch example above the boundary theory is well defined. Possible to describe a crunch.
• It is well defined on a world volume which is dS but there is no gravitational coupling.
• To see the crunch change coordinates on the boundary.
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In the dS frame:
• The World Volume expands(consider a slow expansion relative to other scales).
• Time extends from -∞ to ∞
• The couplings in the Lagrangian are time INDEPENDENT
In the E frame:
• The world volume is static when it exists.
• Time has a finite extension.
• The relevant couplings in the Lagrangian are time dependent and explode at the end of time. The marginal operators remain time independent.
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A simple classical model: O(N) on de Sitter
Phases are clear-cut
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Over at the E-frame...
Mass term blows to in finite time
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• A crunch can be described by a regular QFT on dS or by evolving with a state by a Hamiltonian which is well defined for a finite time range and then ceases to exist.
• The two Hamiltonians do NOT commute.
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One can build quantum mechanical models with two non-commuting Hamiltonians
t-evolution crunches and τ-evolution is eternal
but they are complementary as both time evolutionoperators are related by a unitary canonical map
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Bulk analogs
bubble of nothingContinues to dS gapand E-decoupling
Domain wall flowContinues to dS condensateand E-crunch
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What about ?
This is the slightly massive UV CFT on a finite box
Detailed dynamics should depend on quantum effectsafter large-N summation
In Bulk, we get linearized scalar flows which crunchfor either sign of
(Maldacena)Small scalar flowsmall large-N dS condensateE-frame still crunches
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• An unstable marginal operator on the boundary is related to a Coleman de Luccia bubble in the bulk.
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• As seen on the boundary this crunch situation involves a flow to infinity at a finite time and need not be healed in the bulk.
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Butterflies
Time dependent butterfly-like boundary potential
•Stable?
•What is the dual theory in the bulk?
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High frequenciesof oscillation
Positive effective potentialfor drift mode
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Stability zones
Instability zones
Free Field theory
Mathieu equation
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•For a < 2q instabilities are cured
•For a > 2q resonances may appear
•For compactified world volume resonances can be avoided (number theory results)
•What about interacting boundary field theory?•It should thermalize
•Go to the bulk
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Expectations• When the boundary theory is unstable, the
bulk would crunch?
• When the boundary theory is stabilized, then the bulk is healed?
• An interacting boundary theory can thermalize and produce a black hole in the bulk?
• Using AdS/CFT dictionary and numerical analysis
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Crunches
Crunch singularities appearing in a finite timefor low frequencies
AdS
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Black holes
Black holes appearingin a short time
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Black holes
Black holes appearingonly after a long time– Waves bouncing back and forth
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Conclusions
• Crunches can be described by complementary non commuting Hamiltonians. With or without drama.
• Time dependent boundary Hamiltonians can heal crunch singularities.