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有限温度AdS/CFT: why interesting?
192005 DEC
夏梅 誠(KEK)
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Spacetime w/boundary
Boundary: no GravityGravity interior: due to “color”
Interior has Gravity
マルダセナ「重力は幻なのか?」日経サイエンス2006年2月号(夏梅訳)より
information interior: encoded in boundary as well
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Why interesting?
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Two sides of AdS/CFT
Gauge Theory Gravity
Gauge Theory Gravity
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Puzzles of BH such as
singularity probleminformation paradox
...
Gauge theory is expected to deconfine at high temperature.Dynamics of gauge theory plasmas
Experiments underway (RHIC)
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RHIC complex
RHIC: Relativitistic Heavy Ion Collider (Bookhaven National Nab.)
heavy ion: e.g. 197Au
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http://www.bnl.gov/RHIC/RHIC_complex.htm
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A STAR event
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Animation courtesy of the STAR Experiment at Brookhaven National Laboratory's Relativistic Heavy Ion Collider
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Goal: realize deconfinement transition (quark-gluon plasma)
Press release (April 18, 2005):
"instead of behaving like a gas of free quarks and gluons, as was expected, the matter created in RHIC’s heavy ion collisions appears to be more like a liquid."
"The possibility of a connection between string theory and RHIC collisions is unexpected and exhilarating," (Director of the DOE Office of Science)
APS annual meeting 2005
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First time string theory has been mentioned in the announcement of a major experiment
How is string theory related to quark-gluon plasma?
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Original AdS/CFT:
N=4 SYM ⇔ Type IIB on AdS
Finite temperature:
N=4 SYM at finite temp. ⇔ Type IIB on AdS black hole
thermal thermal due to the Hawking radiation
Motivated from the D3-brane
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But usual BHs (e.g. Schwarzschild)
thermal equilibrium: impossible due to negative specific heat (characteristic of gravity)
C=dM/dT<0
Smaller BHs have higher temperature
Reason why AdS BHs (positive specific heat)
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Main evidences of finite temp. AdS/CFT
Gauge theory is expected to deconfine at high temperature
2 order parameters for deconfinement
Polyakov loops
• (finite temperature version of Wilson loop)
Large-Nc dependence of free energy
F ~ O(Nc2) in plasma phase
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0
!
Polyakov loop
Witten (1998)
€
P ≠ 0
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Shortcomings
Only qualitative understanding (due to lack of SUSY)
thermodynamic properties computed, but nonequilibrium processes?
Gauge theories other than N=4 SYM: less understood(Even T=0 backgrounds are quite involved for N<4)
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Kovtun - Starinets - Son (2004)and many others
There is a claim to solve these problems all at once.
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Towards equilibrium
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SYM → thermalize again “relaxation time”
BH → perturbations decay and always return to “thermal equilibrium” (Stationary BHs are unique due to no-hair thms. )
SYM and BH respond similarly under perturbations
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Add perturbations
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hydrodynamic pt of view
BH:
Water pond:
The diffusion can be regarded as a consequence of viscosity hydrodynamically
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Fluid bet. 2 plates and move the upper plate
The lower plate experiences a force
microscopically: momentum transfer
Viscosity
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v
L
↓(shear) viscosity
€
FA
= ηvL
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But viscosity of what?
The notion of “viscosity” can be considered for BHs.
BH in reality is a vacuum solution and does not really have viscosity
Possibility 1: viscosity of membrane
Horizon can be regarded as a physical membrane w/ viscosity.
“Membrane paradigm”
Possibility 2: viscosity of dual gauge theory plasma
⇒ plasma viscosity: calculable from BH
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Viscosity from AdS/CFT
In Gravity, the diffusion occurs by BH absorption
shear viscosity ⇔ absorption cross section by BH = horizon area
entropy ⇔ horizon area
Each relation is a general result, so this is
A universal result
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Kovtun - Starinets - Son (2004)and many others
€
ηs
=h
4πkB
Das - Gibbons - Mathur (1997)
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The claim:
Gauge theory plasmas which have gravity duals: universal low value of shear viscosity
at large ’t Hooft coupling (for zero chemical potential)
Gravity dual of QCD: unknown
→ but this result can be compared w/ experiments
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RHIC may suggest
Close to the AdS/CFT duality value (1/4π)
: still strongly-coupled
so the duality may be useful to analyze QGP
if they really form QGP and if hydrodymanic interpretation is correct
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€
T ~ O(ΛQCD )
€
ηs~ 0.1× h
kB?
Implications for quark-gluon plasma?
Teaney (2003)
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Behavior at weak coupling
Strong coupling prediction:
In general,
η ~ (mass density) × (mean velocity) × (mean free path) ↓ weak coupling larger
Momentum transfer: more effective
So, at weak coupling
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€
ηs
>>h
4πkB
€
ηs
=h
4πkB
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Viscosity bound
For gauge theory plasmas, we obtain
The inequality is saturated at strong coupling.
A conjecture: any fluid satisfies
cf. Water under normal conditions:
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€
ηs≥
h
4πkB
€
ηs~ (3×103)× h
4πkB
€
ηs≥
h
4πkB
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More examples
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1 1 0 100 1000T, K
0
50
100
150
200
Helium 0.1MPaNitrogen 10MPa
Water 100MPa
Viscosity bound
4! "
sh
Adapted from hep-th/0405231
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Rough argument
The existence of the bound itself is natural
⇒ valid for fluids w/ quasiparticle description
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€
⇒ lmfp > λdeBroglie
€
ηs
~ mv lmfp > h
€
η ~ ρv lmfp
s ~ ρm
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Finite-temperature AdS/CFT
• interesting to study puzzles of BHs
• interesting to study gauge theory plasmas
AdS/CFT may be useful to analyze experimentsExperiments may be useful to confirm AdS/CFT
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Summary