Emergent SpaceTime and and Induced Gravity

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Emergent Space-Time and and Induced Gravity
Madrid , November 17th, 2006

• Some (Speculative) Ideas on
• Strings versus Cosmology

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(No Transcript)
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Standard (inflationary) cosmology is
successfull.It uses low energy effective action,
and needs very little input from string theory.
Strings versus Cosmology

• My personal view
• Dont be satisfied to with using low energy
  action,
• but use the complete (microscopic) string theory
• to challenge the basic assumptions on which
• standard cosmology (including inflation) is
  based.

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String theory needs concrete problems
Strings versus Cosmology

• Black Holes led to important progress
  (AdS/CFT).
• drastic departure from
  old views.
• (complementarity,
  holography, unitarity.)

(collapse, information loss, baby universes.)

• Cosmology still in its infancy, no
  breakthrough yet.
• expect drastic
  departure from old views.
• (initial conditions,
  inflation, multiverse.)

(complementarity, holography, unitarity.)
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String theory indicates that
Strings versus Cosmology

• Space-time is emergent
• Gravity is induced

• What does this mean for cosmology?
• What was the Big Bang? (if it ever
  happened)
• How does space-time emerge?
• Is the emergent space-time observer
  dependent?
• Is there a unitary quantum system underlying
  all this?
• Will this be at all important for
  observations?

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Outline

• Part I Observer complementarity . Parikh ,
  EV (04)
• A Model for de Sitter space
• Part II Emergent Space-Time
• The Matrix Big Bang
  Craps, Sethi, EV (05)
• Part III Induced Gravity
• The Black Hole Farey Tail.
  Dijkgraaf, Moore,Maldacena, EV (00)
• 
  de Boer, Cheng,
  Dijkgraaf, Manschot, EV (06)
• 
  
  
• 
  

Part IV A Heretic View on Cosmology
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I A Model for de Sitter space
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Every eternal observer has complete knowledge
about the quantum state of the Universe.
Observer complementarity
No quantum states correspond to physics outside
the maximal causal diamant.
Observers agree on probabilities for events, but
not necessarily on their interpretation.
Classical space-time is only an approximate
notion and may be different for different
observers.
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Model for de Sitter space

• Every observer has a finite dimensional Hilbert
  space

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Model for de Sitter space

• The Hilbert space is reps of SO(d-1)

forms a reps of SO(d,1).

• A concrete model can be made using a
• spinor field on the (d-1)-dim
  spatial sphere

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II The Matrix Big Bang
weakly coupled strings
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Lightlike Linear Dilaton
10d metric dilaton
Lift to M-theory
in new lightcone coordinates
null singularity
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Matrix dual of lightlike linear dilaton in DLCQ
Matrix String (11)d super Yang-Mills
/
light-cone momentum
string coupling
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III The Black Hole Farey Tail
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Extremal Black Hole
Near horizon geometry
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Black holes in string and M-theory.

• M-theory on CY
• M2-branes wrapping 2-cycles
• M5-branes wrapping 4-cycles
• ? 5d black strings
• 4d black hole 5d black string wrapping circle.
• World volume theory 2d CFT
• (Maldacena, Strominger,Witten)
• Holographic dual to near horizon geometry

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An Exact Asymptotic Formula
Then we have
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Thermal AdS3 vs. BTZ
Periodic identification
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SL(2,Z) orbit of AdS Black Holes

• Different euclidean black holes distinguished
  by non-contractible cycle
• Euclidean action

Maldacena, Strominger
AdS3/CFT2
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Farey tail Z(t) sum over SL(2,Z) orbit of
black holes
contribution of each black hole geometry
subleading corrections black hole dressed
with light particle states that do not form black
holes
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IV A Heretic View on Cosmology
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Standard Big BangModel
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observer
past lightcone
Early Universe
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(No Transcript)
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Geometry of Universe is derived from OUR
OBSERVATIONS
From our perspective we are in the middle of our
Universe
Can one interprete the cosmological data in an
STATIC isotropic but non-homogenous (!)
cosmological model?
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brane worlds can live in a static
background.
one adds scale as fifth dimension.
Idea We live in a static five dimensional space.
The apparent expansion of the Universe is caused
by the fact that for more distant objects the
observed signals are coming from bigger scales.
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RULE at every time step re-throw one
dice.QUESTION What is the most likely state
at the following time
step?
previous
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The End