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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