Transport in strongly coupled QFTsand

gauge/gravity duality

Andrei Starinets

Moscow State UniversityMoscowRussia

22 August 2009

Rudolf Peierls Centre for Theoretical Physics

Oxford University

XIV Lomonosov Conference

Heavy ion collision experiments at RHIC (2000-current) and LHC (2009-??)create hot and dense nuclear matter known as the “quark-gluon plasma”

Evolution of the plasma “fireball” is described by relativistic fluid dynamics

(note: qualitative difference between p-p and Au-Au collisions)

Need to know

thermodynamics (equation of state)kinetics (first- and second-order transport coefficients)in the regime of intermediate coupling strength:

(relativistic Navier-Stokes equations): Landau; Bjorken

initial conditions (initial energy density profile)thermalization time (start of hydro evolution)

freeze-out conditions (end of hydro evolution)

Elliptic flow, jet quenching… - focus on transport in this talk

Quantum field theories at finite temperature/density

Equilibrium Near-equilibrium

entropyequation of state

…….

transport coefficientsemission rates

………

perturbative non-perturbativepQCD Lattice

perturbative non-perturbativekinetic theory ????

Thermodynamics Kinetics

Figure: an artistic impression from Myers and Vazquez, 0804.2423 [hep-th]

Energy density vs temperature for various gauge theories

Ideal gasof quarksand gluons

Ideal gasof hadrons

AdS/CFT correspondence

conjecturedexact equivalence

Generating functional for correlationfunctions of gauge-invariant operators String partition function

In particular

Classical gravity action serves as a generating functional for the gauge theory correlators

Latest test: Janik’08

• Field content:

• Action:

Gliozzi,Scherk,Olive’77Brink,Schwarz,Scherk’77

(super)conformal field theory = coupling doesn’t run

supersymmetric YM theory

Dual to QCD? (Polchinski-Strassler)

coupling

energy

Dual to QCD? (Polchinski-Strassler)

coupling

energy

Dual to QCD? (Polchinski-Strassler)

coupling

energy

At zero temperature, N=4 SYM is obviously a very bad approximation to QCD

At finite temperature it is qualitatively similar to QCD

non-Abelian plasma (with additional d.o.f.)

area law for spatial Wilson loops

Debye screening

spontaneous breaking of symmetry at high temperature

supersymmetry broken

However:

hydrodynamics

Hydrodynamics: fundamental d.o.f. = densities of conserved charges

Need to add constitutive relations!

Example: charge diffusion

[Fick’s law (1855)]

Conservation law

Constitutive relation

Diffusion equation

Dispersion relation

Expansion parameters:

First-order transport (kinetic) coefficients

* Expect Einstein relations such as to hold

Shear viscosity

Bulk viscosity

Charge diffusion constant

Supercharge diffusion constant

Thermal conductivity

Electrical conductivity

Second-order transport (kinetic) coefficients

Relaxation time

Second order trasport coefficient

Second order trasport coefficient

Second order trasport coefficient

Second order trasport coefficient

(for theories conformal at T=0)

In non-conformal theories such as QCD, the total number of second-order transportcoefficients is quite large

M,J,QHolographically dual system

in thermal equilibrium

M, J, Q

T S

Gravitational fluctuations Deviations from equilibrium

????

and B.C.

Quasinormal spectrum

10-dim gravity4-dim gauge theory – large N,

strong coupling

Computing transport coefficients from “first principles”

Kubo formulae allows one to calculate transportcoefficients from microscopic models

In the regime described by a gravity dual the correlator can be computed using

the gauge theory/gravity duality

Fluctuation-dissipation theory(Callen, Welton, Green, Kubo)

Example: stress-energy tensor correlator in

in the limit

Finite temperature, Mink:

Zero temperature, Euclid:

(in the limit )

The pole (or the lowest quasinormal freq.)

Compare with hydro:

In CFT:

Also, (Gubser, Klebanov, Peet, 1996)

First-order transport coefficients in N = 4 SYMin the limit

Shear viscosity

Bulk viscosity

Charge diffusion constant

Supercharge diffusion constant

Thermal conductivity

Electrical conductivity

(G.Policastro, 2008)

for non-conformal theories see Buchel et al; G.D.Moore et al

Gubser et al.

Shear viscosity in SYM

Correction to : Buchel, Liu, A.S., hep-th/0406264

perturbative thermal gauge theoryS.Huot,S.Jeon,G.Moore, hep-ph/0608062

Buchel, 0805.2683 [hep-th]; Myers, Paulos, Sinha, 0806.2156 [hep-th]

Electrical conductivity in SYM

Weak coupling:

Strong coupling:

* Charge susceptibility can be computed independently:

Einstein relation holds:

D.T.Son, A.S., hep-th/0601157

Universality ofTheorem:For a thermal gauge theory, the ratio of shear viscosity to entropy density is equal to in the regime described by a dual gravity theory

Remarks:

• Extended to non-zero chemical potential:

• Extended to models with fundamental fermions in the limit

• String/Gravity dual to QCD is currently unknown

Benincasa, Buchel, Naryshkin, hep-th/0610145

Mateos, Myers, Thomson, hep-th/0610184

Universality of shear viscosity in the regime described by gravity duals

Graviton’s component obeys equation for a minimally coupled massless scalar. But then .Since the entropy (density) is we get

Three roads to universality of

The absorption argumentD. Son, P. Kovtun, A.S., hep-th/0405231

Direct computation of the correlator in Kubo formula from AdS/CFT A.Buchel, hep-th/0408095

“Membrane paradigm” general formula for diffusion coefficient + interpretation as lowest quasinormal frequency = pole of the shear mode correlator + Buchel-Liu theoremP. Kovtun, D.Son, A.S., hep-th/0309213, A.S., 0806.3797 [hep-th],P.Kovtun, A.S., hep-th/0506184, A.Buchel, J.Liu, hep-th/0311175

Chernai, Kapusta, McLerran, nucl-th/0604032

A viscosity bound conjecture

P.Kovtun, D.Son, A.S., hep-th/0309213, hep-th/0405231

Minimum of in units of

?

A hand-waving argument

Gravity duals fix the coefficient:

Thus ?

Shear viscosity - (volume) entropy density ratiofrom gauge-string duality

In particular, in N=4 SYM:

In ALL theories (in the limit where dual gravity valid) :

Y.Kats and P.Petrov: 0712.0743 [hep-th]

M.Brigante, H.Liu, R.C.Myers, S.Shenker and S.Yaida: 0802.3318 [hep-th], 0712.0805 [hep-th].

Other higher-derivative gravity actions

R.Myers,M.Paulos, A.Sinha: 0903.2834 [hep-th] (and ref. therein – many other papers)

for superconformal Sp(N) gauge theory in d=4

Also: The species problem: T.Cohen, hep-th/0702136; A. Dolbado, F.Llanes-Estrada: hep-th/0703132

Shear viscosity - (volume) entropy density ratio in QCD

The value of this ratio strongly affects the elliptic flow in hydro models of QGP

Viscosity-entropy ratio of a trapped Fermi gas

0.2 0.4 0.6 0.8

0.1

0.2

0.3

0.4

0.5

0.6

0.7

η/s

T/TF

T.Schafer, cond-mat/0701251

(based on experimental results by Duke U. group, J.E.Thomas et al., 2005-06)

Vis

cosi

ty “m

easu

rem

ents

”at R

HIC

01

23

40510152025

p T (

GeV

)

v2 (%)

ST

AR

PH

EN

IX

EO

S Q

EO

S H

h+/−

Vis

cosi

ty is

ON

E o

f the

par

amet

ers

used

in th

e hy

dro

mod

els

desc

ribin

g th

e az

imut

hala

niso

tropy

of p

artic

le d

istri

butio

n

-elli

ptic

flow

for

parti

cle

spec

ies

“i”

Elli

ptic

flow

repr

oduc

ed fo

r

e.g.

Bai

er, R

omat

schk

e, n

ucl-t

h/06

1010

8

Per

turb

ativ

eQ

CD

:

SY

M:

Che

rnai

, Kap

usta

, McL

erra

n, n

ucl-t

h/06

0403

2

01

23

4p T

[GeV

]

05101520253035v2 (percent)

STA

R n

on-f

low

cor

rect

ed (

est)

.ST

AR

eve

nt-p

laneC

GC

η/s=

10-4

η/s=

0.08

η/s=

0.16

η/s=

0.24

Luzu

man

d R

omat

schk

e, 0

804.

4015

[nuc

-th]

Elli

ptic

flow

with

col

or g

lass

con

dens

ate

initi

al c

ondi

tions

01

23

4p T

[GeV

]

0510152025v2 (percent)

STA

R n

on-f

low

cor

rect

ed (

est.)

STA

R e

vent

-pla

neGla

uber

η/s=

10-4

η/s=

0.08

η/s=

0.16

Luzu

man

d R

omat

schk

e, 0

804.

4015

[nuc

-th]

Elli

ptic

flow

with

Gla

uber

initi

al c

ondi

tions

Vis

cosi

ty/e

ntro

py ra

tio in

QC

D: c

urre

nt s

tatu

s

QC

D:R

HIC

elli

ptic

flow

ana

lysi

s su

gges

ts

Theo

ries

with

gra

vity

dua

ls in

the

regi

me

whe

re th

e du

al g

ravi

ty d

escr

iptio

n is

val

id

(uni

vers

al li

mit)

QC

D:(

Indi

rect

) LQ

CD

sim

ulat

ions

H.M

eyer

, 080

5.45

67 [h

ep-th

]

Trap

ped

stro

ngly

cor

rela

ted

cold

alk

ali a

tom

s

Liqu

id H

eliu

m-3

T.S

chaf

er, 0

808.

0734

[nuc

l-th]

[Kov

tun,

Son

& A

.S] [

Buc

hel]

[Buc

hel &

Liu

, A.S

]

Spe

ctra

l sum

rule

s fo

r the

QG

P

0.5

1

123456

0.1

0.2

0.1

0.05

w0.5

11.5

w

2468

10

P.R

omat

schk

e, D

.Son

, 090

3.39

46 [h

ep-p

h]

In N

=4 S

YM

at A

NY

cou

plin

g

Pho

topr

oduc

tion

rate

in S

YM

02

46

8k

�T

0.005

0.01

0.015

0.02

d�Γ�dk�ΑEMNc2T3�

�1

SYM,

Λ�

�

SYM,

Λ0.5

SYM,

Λ0.2

(Nor

mal

ized

) pho

ton

prod

uctio

n ra

te in

SY

M fo

r var

ious

val

ues

of‘t

Hoo

ftco

uplin

g

Oth

er a

venu

es o

f (re

late

d) re

sear

ch

Bul

k vi

scos

ity fo

r non

-con

form

al th

eorie

s (B

uche

l, B

enin

casa

, Gub

ser,

Moo

re…

)

Non

-rel

ativ

istic

gra

vity

dua

ls (S

on, M

cGre

evy,

…)

Gra

vity

dua

ls o

f the

orie

s w

ith S

SB

, AdS

/CM

T (K

ovtu

n, H

erzo

g, H

artn

oll,

Hor

owitz

…)

Bul

k fro

m th

e bo

unda

ry, t

ime

evol

utio

n of

QG

P (J

anik

,…)

Nav

ier-

Sto

kes

equa

tions

and

thei

r gen

eral

izat

ion

from

gra

vity

(Min

wal

la,…

)

Qua

rks

mov

ing

thro

ugh

plas

ma

(Che

sler

, Yaf

fe, G

ubse

r,…)

S. H

artn

oll

“Lec

ture

s on

hol

ogra

phic

met

hods

for c

onde

nsed

mat

ter p

hysi

cs”,

0903

.324

6 [h

ep-th

]

C. H

erzo

g“L

ectu

res

on h

olog

raph

ic s

uper

fluid

ityan

d su

perc

ondu

ctiv

ity”,

0904

.197

5 [h

ep-th

]

M. R

anga

man

i“G

ravi

ty a

nd h

ydro

dyna

mic

s: L

ectu

res

on th

e flu

id-g

ravi

ty c

orre

spon

denc

e”,

0905

.435

2 [h

ep-th

]

New

dire

ctio

ns

THA

NK

YO

U

Hyd

rody

nam

ic p

rope

rties

of s

trong

ly in

tera

ctin

g ho

t pla

smas

in 4

dim

ensi

ons

can

be re

late

d (fo

r cer

tain

mod

els!

)

to fl

uctu

atio

ns a

nd d

ynam

ics

of 5

-dim

ensi

onal

bla

ck h

oles

AdS

/CFT

cor

resp

onde

nce:

the

role

of J

satis

fies

linea

rized

supe

rgra

vity

e.o.

m. w

ith b

.c.

For a

giv

en o

pera

tor

, i

dent

ify th

e so

urce

fiel

d ,

e.g

.

To c

ompu

te

corre

lato

rsof

,

one

nee

ds to

sol

ve th

e bu

lksu

perg

ravi

tye.

o.m

. for

and

com

pute

the

on-s

hell

actio

nas

a fu

nctio

nal o

f the

b.c

.

Then

, tak

ing

func

tiona

l der

ivat

ives

of

giv

es

The

reci

pe:

War

ning

:e.o

.m. f

or d

iffer

ent b

ulk

field

s m

ay b

e co

uple

d: n

eed

self-

cons

iste

nt s

olut

ion

Hol

ogra

phy

at fi

nite

tem

pera

ture

and

den

sity

Non

zero

exp

ecta

tion

valu

es o

f ene

rgy

and

char

ge d

ensi

ty tr

ansl

ate

into

nont

rivia

l bac

kgro

und

valu

es o

f the

met

ric (a

bove

ext

rem

ality

)=ho

rizon

and

elec

tric

pote

ntia

l = C

HA

RG

ED

BLA

CK

HO

LE (w

ith fl

at h

oriz

on)

tem

pera

ture

of t

he d

ual g

auge

theo

ry

chem

ical

pot

entia

l of t

he d

ual t

heor

y

Gau

ge-s

tring

dua

lity

and

QC

D

App

roac

h I:

use

the

gaug

e-st

ring

(gau

ge-g

ravi

ty) d

ualit

y to

stu

dyN

=4 S

YM

and

sim

ilar t

heor

ies,

get

qua

litat

ive

insi

ghts

into

rele

vant

asp

ects

of Q

CD

, loo

k fo

r uni

vers

al q

uant

ities

App

roac

h II:

botto

m-u

p (a

.k.a

. AdS

/QC

D) –

star

t with

QC

D, b

uild

gra

vity

dua

l ap

prox

imat

ion

App

roac

h III

:sol

ve Q

CD

App

roac

h III

a: p

QC

D(w

eak

coup

ling;

pro

blem

s w

ith c

onve

rgen

ce fo

r the

rmal

qua

ntiti

es)

App

roac

h III

b: L

QC

D (u

sual

latti

ce p

robl

ems

+ pr

oble

ms

with

kin

etic

s)

(exa

ct s

olut

ions

but

lim

ited

set o

f the

orie

s)

(unl

imite

d se

t of t

heor

ies,

app

roxi

mat

e so

lutio

ns, s

yste

mat

ic p

roce

dure

unc

lear

)

(will

not c

onsi

der h

ere

but s

ee e

.g. G

ürso

y, K

irits

is, M

azza

nti,

Nitt

i, 09

03.2

859

[hep

-th])

Ove

r the

last

sev

eral

yea

rs, h

olog

raph

ic (g

auge

/gra

vity

dua

lity)

met

hods

wer

e us

ed to

stu

dy s

trong

ly c

oupl

ed g

auge

theo

ries

at fi

nite

tem

pera

ture

and

dens

ity

Thes

e st

udie

s w

ere

mot

ivat

ed b

y th

e he

avy-

ion

colli

sion

pro

gram

s at

RH

ICan

d LH

C (A

LIC

E, A

TLA

S) a

nd th

e ne

cess

ity to

und

erst

and

hot a

nd d

ense

nucl

ear m

atte

r in

the

regi

me

of in

term

edia

te c

oupl

ing

As

a re

sult,

we

now

hav

e a

bette

r und

erst

andi

ng o

f the

rmod

ynam

ics

and

espe

cial

ly k

inet

ics

(tran

spor

t) of

stro

ngly

cou

pled

gau

ge th

eorie

s

Of c

ours

e, th

ese

calc

ulat

ions

are

don

e fo

r the

oret

ical

mod

els

such

as

N=4

SY

Man

d its

cou

sins

(inc

ludi

ng n

on-c

onfo

rmal

theo

ries

etc)

.

We

don’

t kno

w q

uant

ities

suc

h as

for Q

CD

New

tran

spor

t coe

ffici

ents

in

Sou

nd d

ispe

rsio

n:

Kub

o:

SY

M

Per

turb

atio

nth

eory

Latti

ce

Our

und

erst

andi

ng o

f gau

ge th

eorie

s is

lim

ited…

Per

turb

atio

nth

eory

Latti

ce

Con

ject

ure:

sp

ecifi

c ga

uge

theo

ry in

4 d

im =

spec

ific

strin

g th

eory

in 1

0 di

m

Per

turb

atio

nth

eory

Latti

ce

Dua

l gra

vity

In p

ract

ice:

gra

vity

(low

ene

rgy

limit

of s

tring

theo

ry) i

n 10

dim

=4-

dim

gau

ge th

eory

in a

regi

on o

f a p

aram

eter

spa

ce

Can

add

fund

amen

tal f

erm

ions

with

Com

putin

g re

al-ti

me

corr

elat

ion

func

tions

from

gr

avity

To e

xtra

ct tr

ansp

ort c

oeffi

cien

ts a

nd s

pect

ral f

unct

ions

from

dua

l gra

vity

,w

e ne

ed a

reci

pe fo

r com

putin

g M

inko

wsk

ispa

ce c

orre

lato

rsin

AdS

/CFT

The

reci

pe o

f [D

.T.S

on&

A.S

., 20

01]a

nd [C

.Her

zog

& D

.T.S

on, 2

002]

rela

tes

real

-tim

e co

rrel

ator

sin

fiel

d th

eory

to P

enro

se d

iagr

am o

f bla

ck h

ole

in d

ual g

ravi

ty

Qua

sino

rmal

spec

trum

of d

ual g

ravi

ty =

pol

es o

f the

reta

rded

cor

rela

tors

in 4

d th

eory

[D.T

.Son

& A

.S.,

2001

]

Exa

mpl

e: R

-cur

rent

cor

rela

tori

nin

the

limit

Zero

tem

pera

ture

:

Fini

te te

mpe

ratu

re:

Pol

es o

f

=

qua

sino

rmal

spec

trum

of d

ual g

ravi

ty b

ackg

roun

d

(D.S

on, A

.S.,

hep-

th/0

2050

51,

P.K

ovtu

n, A

.S.,

hep-

th/0

5061

84)

Ana

lytic

stru

ctur

e of

the

corre

lato

rs

ωω

− i

8

− i

12

− i

4

T −

> 0

ω

−p

p

p −

> 0

πΤ πΤ

πΤ

− i

8

− i

12

− i

4πΤ πΤ

πΤ

−p

p

Wea

k co

uplin

g: S

. Har

tnol

land

P. K

umar

, hep

-th/0

5080

92ω

−p

p

Stro

ng c

oupl

ing:

A.S

., he

p-th

/020

7133

Com

putin

g tra

nspo

rt co

effic

ient

s fro

m d

ual g

ravi

ty

Ass

umin

g va

lidity

of t

he g

auge

/gra

vity

dua

lity,

al

l tra

nspo

rt co

effic

ient

s ar

e co

mpl

etel

y de

term

ined

by

the

low

est f

requ

enci

esin

qua

sino

rmal

spec

tra o

f the

dua

l gra

vita

tiona

l bac

kgro

und

This

det

erm

ines

kin

etic

s in

the

regi

me

of a

ther

mal

theo

ryw

here

the

dual

gra

vity

des

crip

tion

is a

pplic

able

(D.S

on, A

.S.,

hep-

th/0

2050

51,

P.K

ovtu

n, A

.S.,

hep-

th/0

5061

84)

Tran

spor

t coe

ffici

ents

and

qua

sipa

rticl

esp

ectra

can

als

o be

obta

ined

from

ther

mal

spe

ctra

l fun

ctio

ns

Spe

ctra

l fun

ctio

n an

d qu

asip

artic

les

12

3w

-0.2

0.2

0.4

0.6

0.8

0.5

1

123456

0.1

0.2

0.1

0.05

w

0.5

11.5

w

2468

10

A

B

CA

: sca

lar c

hann

el

B: s

cala

r cha

nnel

-th

erm

al p

art

C: s

ound

cha

nnel

Is th

e bo

und

dead

?Y

.Kat

san

d P

.Pet

rov,

071

2.07

43 [h

ep-th

]“E

ffect

of c

urva

ture

squ

ared

cor

rect

ions

in A

dSon

the

visc

osity

of t

he d

ual g

auge

theo

ry”

supe

rcon

form

alS

p(N

) gau

ge th

eory

in d

=4

M.~

Brig

ante

, H.~

Liu,

R.~

C.~

Mye

rs, S

.~S

henk

eran

d S

.~Y

aida

,``T

he V

isco

sity

Bou

nd a

nd C

ausa

lity

Vio

latio

n,''

0802

.331

8 [h

ep-th

],``V

isco

sity

Bou

nd V

iola

tion

in H

ighe

r Der

ivat

ive

Gra

vity

,'' 07

12.0

805

[hep

-th].

The

“spe

cies

pro

blem

”T.

Coh

en, h

ep-th

/070

2136

, A.D

obad

o, F

.Lla

nes-

Est

rada

, hep

-th/0

7031

32

A v

isco

sity

bou

nd c

onje

ctur

e

P.K

ovtu

n, D

.Son

, A.S

., he

p-th

/030

9213

, hep

-th/0

4052

31

Min

imum

of

i

n un

its o

f

Che

rnai

, Kap

usta

, McL

erra

n, n

ucl-t

h/06

0403

2

Che

rnai

, Kap

usta

, McL

erra

n, n

ucl-t

h/06

0403

2

QC

D

She

ar v

isco

sity

at n

on-z

ero

chem

ical

pot

entia

l

0.1

0.2

0.3

0.4

0.5

1.05

1.1

1.15

1.2

1.25

Rei

ssne

r-N

ords

trom

-AdS

blac

k ho

le

with

thre

e R

cha

rges

(Beh

rnd,

Cve

tic, S

abra

, 199

8)

We

still

hav

e

J.M

asD

.Son

, A.S

.O

.Sar

emi

K.M

aeda

, M.N

atsu

ume,

T.O

kam

ura

(see

e.g

. Yaf

fe, Y

amad

a, h

ep-th

/060

2074

)

Pho

ton

and

dile

pton

emis

sion

fro

m s

uper

sym

met

ricY

ang-

Mills

pla

sma

S. C

aron

-Huo

t, P

. Kov

tun,

G. M

oore

, A.S

., L.

G. Y

affe

, hep

-th/0

6072

37

Pho

tons

inte

ract

ing

with

mat

ter:

Pho

ton

emis

sion

from

SY

M p

lasm

a

To le

adin

g or

der i

n

Mim

icby

gau

ging

glo

bal R

-sym

met

ry

Nee

d on

ly to

com

pute

cor

rela

tors

of th

e R

-cur

rent

s

Now

con

side

r stro

ngly

inte

ract

ing

syst

ems

at fi

nite

den

sity

an

d LO

W te

mpe

ratu

re

Pro

bing

qua

ntum

liqu

ids

with

hol

ogra

phy

Qua

ntum

liqu

idin

p+1

dim

Low

-ene

rgy

elem

enta

ry

exci

tatio

nsS

peci

fic h

eat

at lo

w T

Qua

ntum

Bos

e liq

uid

Qua

ntum

Fer

mi l

iqui

d(L

anda

u FL

T)

phon

ons

ferm

ioni

cqu

asip

artic

les

+bo

soni

cbr

anch

(zer

o so

und)

Dep

artu

res

from

nor

mal

Fer

mi l

iqui

d oc

cur i

n

-3+

1 an

d 2+

1 –d

imen

sion

al s

yste

ms

with

stro

ngly

cor

rela

ted

elec

trons

-In

1+1

–dim

ensi

onal

sys

tem

s fo

r any

stre

ngth

of i

nter

actio

n (L

uttin

gerl

iqui

d)

One

can

app

ly h

olog

raph

y to

stu

dy s

trong

ly c

oupl

ed F

erm

i sys

tem

sat

low

T

L.D

.Lan

dau

(190

8-19

68)

The

sim

ples

t can

dida

te w

ith a

kno

wn

holo

grap

hic

desc

riptio

n is

at fi

nite

tem

pera

ture

T a

nd n

onze

ro c

hem

ical

pot

entia

l ass

ocia

ted

with

the

“bar

yon

num

ber”

dens

ity o

f the

cha

rge

Ther

e ar

e tw

o di

men

sion

less

par

amet

ers:

is th

e ba

ryon

num

ber d

ensi

tyis

the

hype

rmul

tiple

tmas

s

The

holo

grap

hic

dual

des

crip

tion

in th

e lim

it

is

giv

en b

y th

e D

3/D

7 sy

stem

, with

D3

bran

esre

plac

ed b

y th

e A

dS-

Sch

war

zsch

ild g

eom

etry

and

D7

bran

esem

bedd

ed in

it a

s pr

obes

.

Kar

ch&

Kat

z, h

ep-th

/020

5236

AdS

-Sch

war

zsch

ild b

lack

hol

e (b

rane

) bac

kgro

und

D7

prob

e br

anes

The

wor

ldvo

lum

eU

(1) f

ield

c

oupl

es to

the

flavo

r cur

rent

at th

e bo

unda

ry

Non

trivi

al b

ackg

roun

d va

lue

of

c

orre

spon

ds to

non

trivi

al e

xpec

tatio

n va

lue

of

We

wou

ld li

ke to

com

pute

-the

spe

cific

hea

t at l

ow

tem

pera

ture

-the

cha

rge

dens

ity c

orre

lato

r

The

spec

ific

heat

(in

p+1

dim

ensi

ons)

:

(not

e th

e di

ffere

nce

with

Fer

mi

an

d B

ose

sy

stem

s)

The

(reta

rded

) cha

rge

dens

ity c

orre

lato

rha

s a

pole

cor

resp

ondi

ng to

a p

ropa

gatin

g m

ode

(zer

o so

und)

-eve

n at

zer

o te

mpe

ratu

re

(not

e th

at th

is is

NO

T a

supe

rflui

dph

onon

who

se a

ttenu

atio

n sc

ales

as

)

New

type

of q

uant

um li

quid

?

Epi

logu

eO

n th

e le

vel o

f the

oret

ical

mod

els,

ther

e ex

ists

a c

onne

ctio

nbe

twee

n ne

ar-e

quili

briu

m re

gim

e of

cer

tain

stro

ngly

cou

pled

th

erm

al fi

eld

theo

ries

and

fluct

uatio

ns o

f bla

ck h

oles

This

con

nect

ion

allo

ws

us to

com

pute

tran

spor

t coe

ffici

ents

for t

hese

theo

ries

The

resu

lt fo

r the

she

ar v

isco

sity

turn

s ou

t to

be u

nive

rsal

for a

ll su

ch th

eorie

s in

the

limit

of in

finite

ly s

trong

cou

plin

g

At t

he m

omen

t, th

is m

etho

d is

the

only

theo

retic

al to

ol

avai

labl

e to

stu

dy th

e ne

ar-e

quili

briu

m re

gim

e of

stro

ngly

coup

led

ther

mal

fiel

d th

eorie

s

Influ

ence

s ot

her f

ield

s (h

eavy

ion

phys

ics,

con

dmat

)

A h

and-

wav

ing

argu

men

t

Gra

vity

dua

ls fi

x th

e co

effic

ient

:

Thus

Out

look

Gra

vity

dua

l des

crip

tion

of th

erm

aliz

atio

n?

Gra

vity

dua

ls o

f the

orie

s w

ith fu

ndam

enta

l fer

mio

ns:

-pha

se tr

ansi

tions

-hea

vy q

uark

bou

nd s

tate

s in

pla

sma

-tra

nspo

rt pr

oper

ties

Fini

te ‘t

Hoo

ftco

uplin

g co

rrec

tions

to p

hoto

n em

issi

on s

pect

rum

Und

erst

andi

ng 1

/N c

orre

ctio

ns

Pho

nino

Equ

atio

ns s

uch

as

desc

ribe

the

low

ene

rgy

li

mit

of s

tring

theo

ry

As

long

as

the

dila

ton

is s

mal

l, an

d th

us th

e st

ring

inte

ract

ions

are

sup

pres

sed,

this

lim

it co

rres

pond

s to

cla

ssic

al 1

0-di

m E

inst

ein

grav

ity c

oupl

ed to

cer

tain

mat

ter f

ield

s su

ch a

s M

axw

ell f

ield

, p-fo

rms,

dila

ton,

ferm

ions

Val

idity

con

ditio

ns fo

r the

cla

ssic

al (s

uper

)gra

vity

appr

oxim

atio

n

-cur

vatu

re in

varia

nts

shou

ld b

e sm

all:

-qua

ntum

loop

effe

cts

(stri

ng in

tera

ctio

ns =

dila

ton)

sho

uld

be s

mal

l:

In A

dS/C

FT d

ualit

y, th

ese

two

cond

ition

s tra

nsla

te in

to

and

The

chal

leng

e of

RH

IC (c

ontin

ued)

Rap

id th

erm

aliz

atio

n

Larg

e el

liptic

flow

Jet q

uenc

hing

Pho

ton/

dile

pton

emis

sion

rate

s

??

4D b

ound

ary

z 0

The

bulk

and

the

boun

dary

in A

dS/C

FT c

orre

spon

denc

e

5D b

ulk

(+5

inte

rnal

dim

ensi

ons)

UV

/IR: t

he A

dSm

etric

is in

varia

nt u

nder

z pl

ays

a ro

le o

f inv

erse

ene

rgy

scal

e in

4D

theo

ry