AdSCFT and transport constants in Expanding QGP

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AdS/CFT and transport constants in Expanding
QGP

• SangJin Sin (Hanyang)
• _at_YITP, 2008.2.11

0707.0601 KY.Kim, SJS, I.Zahed Casalderry-solana
, Teaney,(ph/0605199) Janik,Peschansky,(th/060614
9)
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SQGP in RHIC

• RHIC found Unexpected strong nature of
  interaction in high energy collision.
• Only Lattice or other non-perturbative method can
  do something for it.
• String duality is one of such method.

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Idea of calculation

• Set up Langevin to introduce transport
  coefficients.
• Identify noise correlation functionas two point
  function ltFFgt.
• Use ads/cft to calculate ltFFgt

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Langevin eq.
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Noise v.s Force
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Open/closed duality

• Open string ? gauge theory
• Closed string? gravity
• Cylinder diagram
• ?quantum gauge/classical gravity duality

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D-brane AdS/CFT

• D-brane closed string soliton whose vibration is
  restricted as open string vibration.
• Multiple D-branes
• Open st.?U(N)
• Closed st.?extra-dim.?Holographicwarped
  transverse space? AdS

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Holographic relation
YM?4d Boundary(global co-ord.)
5d AdS bulk
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Finite temperature YM AdS Black hole
Expanding boundary Medium ??Falling
horizon (conformal invariance)
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RHIC and Bjorken set up
Relativistically accelerated heavy nuclei
Central Rapidity Region

• one-dimensional expansion.

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Bjorken System

• Longitudinal Position ??velocity.
• All particles has common proper time
• ? as coordinate

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Bjorken frame

• a frame following the particle

• Bjorken frame is comoving frame.
• Milnor Universe

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Relativistic Hydrodynamics

• Bjorken framelocal rest frame
• where u(1,0,0,0)
• simplies !
• Hydro eq.
• ?

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Gravity dual of Bjorken system

• Find a solution of Einstein eq. in AdSwith zero
  5d energy-momentum tensor.with falling horizon
  as BC.
• Use Hologrphic renormalization to find the
  relation of 5d metric and boundary energy
  momentum tensor.
• Such sol. found by JanikPeschanskySuch sol.
  with viscousity found by
  SJS Nakamura

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Janik-Peschansky sol.
? Falling Horizon solution as desired!
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Quasi-static Form of metric
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New time
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String fluctuation in the frame following a
particle
Boundary
Horizon
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Equation of Motion
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Reduced Boundary action
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Eq.of M for
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Retarded Green FunctionAnd Boundary condition
Need Infalling boundary condition for
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Scheme of Calculation
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The key problem
Infalling fcts are Needed here
u0
Infalling fcts are easily found here
horizon
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Stratege of work
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Normalization of wave function
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Result
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Decorrelation time
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Momentum correlation and Diffusion constant
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Diffusion Rate
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Solution
Cross over is Exponential
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Conclusion

• We considerred Diffusion of heavy quark in a
  expanding medium
• In comoving frame time dependent diffusion
  problem is captured in the retarded Green
  function, which is calculated by AdS/CFT
• Equilibrium is reached exponentially fast.With
  time scale

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Hankel transform
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Hydrodynamic Limit
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WKB Limit