Applications of Holography in Hot Strongly Coupled Plasmas · Condensed Matter Physics...

Applications of Holography in Hot Strongly Coupled Plasmas

MPI, November 18, 2011

- Seminar 2011MPI, Heidelberg

in collaboration with Carlo Ewerz

Konrad SchadeUniversity of Heidelberg

Heavy ion collisions and AdS/CFT

Hong LiuCenter for Theoretical Physics,Massachusetts Institute of Technology,Cambridge, MA 02139, USA

E-mail: hong [email protected]

Abstract.

We review some recent applications of the AdS/CFT correspondence to heavy ioncollisions including a calculation of the jet quenching parameter in N = 4 super-Yang-Mills theory and quarkonium suppression from velocity scaling of the screening lengthfor a heavy quark-antiquark pair. We also briefly discuss di!erences and similaritiesbetween QCD and N = 4 Super-Yang-Mills theory.

Holography, Gauge/Gravity duals, AdS/CFT correspondence, ...

...many realisations, but one concept.- Seminar 2011 MPI, November 18, 2011




Abstract.


Model of a Fermi liquid using gauge-gravity duality

Subir SachdevDepartment of Physics, Harvard University, Cambridge Massachusetts 02138, USA

(Received 4 August 2011; published 21 September 2011)

We use gauge-gravity duality to model the crossover from a conformal critical point to a confining

Fermi liquid, driven by a change in fermion density. The short-distance conformal physics is represented

by an anti–de Sitter geometry, which terminates into a confining state along the emergent spatial direction.

The Luttinger relation, relating the area enclosed by the Fermi surfaces to the fermion density, is shown to

follow from Gauss’s law for the bulk electric field. We argue that all low energy modes are consistent with

Landau’s Fermi liquid theory. An explicit solution is obtained for the Fermi liquid for the case of hard-

wall boundary conditions in the infrared.

DOI: 10.1103/PhysRevD.84.066009 PACS numbers: 11.25.Tq, 71.10.Hf

PHYSICAL REVIEW D 84, 066009 (2011)


...many realisations, but one concept.

MPI, November 18, 2011- Seminar 2011




Abstract.














Vortex flow for a holographic superconductor

Kengo Maeda*

Faculty of Engineering, Shibaura Institute of Technology, Saitama, 330-8570, Japan

Takashi Okamura†

Department of Physics, Kwansei Gakuin University, Sanda, 669-1337, Japan(Received 7 December 2010; published 2 March 2011)

We investigate energy dissipation associated with the motion of the scalar condensate in a holographic

superconductor model constructed from the charged scalar field coupled to the Maxwell field. Upon

application of constant magnetic and electric fields, we analytically construct the vortex-flow solution and

find the vortex-flow resistance near the second-order phase transition where the scalar condensate begins.

The characteristic feature of the nonequilibrium state agrees with the one predicted by the time-dependent

Ginzburg-Landau (TDGL) theory. We evaluate the kinetic coefficient in the TDGL equation along the line

of the second-order phase transition. At zero magnetic field, the other coefficients in the TDGL equation

are also evaluated just below the critical temperature.

DOI: 10.1103/PhysRevD.83.066004 PACS numbers: 11.25.Tq, 74.20.!z, 74.25.!q








Abstract.














Vortex flow for a holographic superconductor

Kengo Maeda*

Faculty of Engineering, Shibaura Institute of Technology, Saitama, 330-8570, Japan

Takashi Okamura†

Department of Physics, Kwansei Gakuin University, Sanda, 669-1337, Japan(Received 7 December 2010; published 2 March 2011)

We investigate energy dissipation associated with the motion of the scalar condensate in a holographic

superconductor model constructed from the charged scalar field coupled to the Maxwell field. Upon

application of constant magnetic and electric fields, we analytically construct the vortex-flow solution and

find the vortex-flow resistance near the second-order phase transition where the scalar condensate begins.

The characteristic feature of the nonequilibrium state agrees with the one predicted by the time-dependent

Ginzburg-Landau (TDGL) theory. We evaluate the kinetic coefficient in the TDGL equation along the line

of the second-order phase transition. At zero magnetic field, the other coefficients in the TDGL equation

are also evaluated just below the critical temperature.

DOI: 10.1103/PhysRevD.83.066004 PACS numbers: 11.25.Tq, 74.20.!z, 74.25.!q


AdS/QCD model from an effective action for open string tachyons

Ioannis Iatrakis,1 Elias Kiritsis,1,2 and Angel Paredes3

1Crete Center for Theoretical Physics, Department of Physics, University of Crete, 71003 Heraklion, Greece2APC, Universite Paris 7, Batiment Condorcet, F-75205, Paris, France (UMR du CNRS 7164)

3Departament de Fısica Fontamental and ICCUB Institut de Ciencies del Cosmos, Universitat de Barcelona,Martı i Franques, 1, E-08028, Barcelona, Spain

(Received 22 March 2010; published 10 June 2010)

We construct a new, simple phenomenological model along the lines of AdS/QCD. The essential new

ingredient is the brane-antibrane effective action including the open string tachyon proposed by Sen [Phys.

Rev. D 68, 066008 (2003).]. Chiral symmetry breaking happens because of tachyon dynamics. We fit a

large number of low-spin meson masses at the 10%–15% level. The only free parameters involved in the

fits correspond to the overall QCD scale and the quark masses. Several aspects of previous models are

qualitatively improved.

DOI: 10.1103/PhysRevD.81.115004 PACS numbers: 11.25.Tq, 11.25.Wx, 12.38.Lg, 12.40.Yx





Holographic Principle e physics in a (d+1)-dimensional volume can be described by a

theory living on the d-dimensional boundary.

e.g.: duality between gauge theories in d-dimension and gravity theories (string theories) in higher dimensions.

Mald

acen

a, 20

03 MPI, November 18, 2011- Seminar 2011

High Energy Physics

AdS/CFT

AdS/QCD Fluid/Gravity CorrespondenceGauge/Gravity Dualities

Condensed Matter Physics

Non-Relativistic AdS/CFT

Non-Fermi liquids using gauge/gravity duality

Zaan

en, 2

007

Practical Realisation of HolographyHolographic Superconductors

Holographic Neutron Stars


High Energy Physics

AdS/CFT

AdS/QCD Fluid/Gravity CorrespondenceGauge/Gravity Dualities

Condensed Matter Physics

Non-Relativistic AdS/CFT

Non-Fermi liquids using gauge/gravity duality

Zaan

en, 2

007

Practical Realisation of HolographyHolographic Superconductors

Holographic Neutron Stars

!/ssimilar

O‘H

ara e

t al.,

2002

ALICE, 2010 MPI, November 18, 2011- Seminar 2011

Gauge/Gravity Duality

d-dim. gauge theory (without gravity)

d+1-dim. gravitational theory

entropy of gauge theory volume

!"

=entropy of gravitational theory

area! !

SU(Nc) N = 4 SYM AdS5 ! S5

ls R


Gauge/Gravity Duality

d-dim. gauge theory (without gravity)

d+1-dim. gravitational theory

entropy of gauge theory volume

strongly coupled QFT weakly coupled gravity

!"

=

! !

Why is that duality useful?

!"

ls R

SU(Nc) N = 4 SYM AdS5 ! S5

! = g2YMNc

! fixed,Nc !" # : gs ! !/Nc

! !" # :

entropy of gravitational theory area


g2YM ! gs , R4

! !l4s ,

R4! l

4

s

QCD super Yang-MillsN = 4

Nc ! "

N = 4

SYM very different from QCD:

Maximally supersymmetric

Conformal theory, coupling is constant

No confinement, no chiral symmetry breaking

for duality


SYM very different from QCD

Maximally supersymmetric

Conformal theory, coupling is constant

No confinement, no chiral symmetry breaking

for duality

At finite T, differences are smaller:

Above 2 QCD almost conformal

No confinement in QCD above

Finite T breaks supersymmetry

N = 4

Nc ! "

Tc

Tc

QCD super Yang-MillsN = 4


Basic Properties of AdS metric:

with being the AdS curvature

AdS5

R

Solution to 5D Einstein-Hilbert action:

z

z = 0

S =1

16!G

!d5x

!"g(R" 2!)


boundaryfield theory

bulk

ds2 =R2

z2

!

! dt2 + d!x2 + dz2"

black hole metric:

with and

AdS5

z

z = 0

z = zh

Solves the same e. o. m.:

Basic Properties of AdS


boundaryfield theory

bulk

TH =1

!zhh = 1!

z4

z4h

ds2 =R2

z2

!

! h dt2 + d!x2 +dz2

h

"

Metric models at finite temperature BH metric at finite temperature:AdS5

model: Kajantie, Tahkokallio, YeeSWT

2-parameter model:

is a solution to vacuum Einstein equations.

DeWolfe, Rosen; Gubser


with and TH =1

!zhds2 =

R2

z2

!

! h dt2 + d!x2 +dz2

h

"

h = 1!z4

z4h

ds2 =R2

z2ecz

2

!

! h dt2 + d!x2 +dz2

h

"

ds2 = e2A(!)!

! h(!) dt2 + d!x2"

+e2B(!)

h(!)d!2

Screening distance in hot moving plasmas

Rajagopal, Liu, Wiedemann

1.0

0.5

0.0

0.5

1.0

x1

1.0

0.5

0.0

0.5

1.0

x2

0

0.2

0.4

0.6

0.8

zh 1

z


Screening distance in hot moving plasmas

Nambu-Goto action:

with


1.0

0.5

0.0

0.5

1.0

x1

1.0

0.5

0.0

0.5

1.0

x2

0

0.2

0.4

0.6

0.8

zh 1

z


Screening distance in hot moving plasmasStatic - pair in a hot moving plasma “wind” blowing in -direction

Nambu-Goto action:

with

qq


1.0

0.5

0.0

0.5

1.0

x1

1.0

0.5

0.0

0.5

1.0

x2

0

0.2

0.4

0.6

0.8

zh 1

z

velocity

orientation angle

v = tanh !

!

x2

v

v


Configuration of the strings

e string configuration coming closer to the horizon is unstable.

1.0

0.5

0.0

0.5

1.0

x1

1.0

0.5

0.0

0.5

1.0

x2

0

0.2

0.4

0.6

0.8

zh 1

z


Lmax

Configuration of the strings

1.0

0.5

0.0

0.5

1.0

x1

1.0

0.5

0.0

0.5

1.0

x2

0

0.2

0.4

0.6

0.8

zh 1

z

1.0

0.5

0.0

0.5

1.0

x1

1.0

0.5

0.0

0.5

1.0

x2

0

0.2

0.4

0.6

0.8

zh 1

z


e string configuration coming closer to the horizon is unstable.

Lmax Lmax

Screening distance boundN = 4Lmax is minimal for .

0 1 2 3 4

0.84

0.86

0.88

0.90

0.92

0.94

!

"Tcosh!!"L m

ax

2#param. String

2#param. Einstein

SWT

N $ 4


0.0 0.2 0.4 0.6 0.85

4

3

2

1

0

LΠT

FΗ, cΛ T

UnstableStable

cT2 0

cT2 6

-free energy: results

Free energy of -pair at finite rapidity .

Unstable configurations are weaker bounded.

QQ

1.0 0.5 0.0 0.5 1.0x11.0

0.5

0.0

0.5

1.0

x2

0

0.2

0.4

0.6

0.8

zh 1

z

qq ! = 1


Coupling is defined as in QCD.

Many possibilities by rescaling the parameters.

!qq

0.02 0.05 0.10 0.20

0.16

0.18

0.20

0.22

0.24

0.26

rfm

Α qq

TTc 4TTc 2TTc 1.4TTc 1.1TTc 1

Running Coupling from Free Energy

!qq =3r2

4

dF (r, T )

dr


0.02 0.05 0.10 0.20

0.16

0.18

0.20

0.22

0.24

0.26

rfm

Α qq

TTc 4TTc 2TTc 1.4TTc 1.1TTc 1

Running Coupling from Free Energy

0

0.1

0.2

0.3

0.4

0.5

0.6

0.01 0.1 0.5

r [fm]

qq (r,T)

Kaczmarek, Karsch, Petreczky and Zantow, 2006


4020

0

20

40

x1

4020

0

20

40

x2

0

10

20

30

z

What can we learn from a rotating quark in a hot moving plasma?

T = 0, ! = 0.3, 0.7, R0 = 1

Rotating Quark at Zero Temperature


Rotating Quark at Finite Temperature

What can we learn from a rotating quark in a hot moving plasma?

T = 0, ! = 0.3, 0.7, R0 = 1 T = 0.01, ! = 0.7, R0 = 1

4020

0

20

40

x1

4020

0

20

40

x2

0

10

20

30

z

40

20

0

20

40

x1

4020

0

20

40

x2

0

10

20

30zh

z


Is energy loss due to synchrotron radiation or due to drag dominant?

What happens in deformed models?

dE/dt is very robust.

4020

0

20

40

x1

4020

0

20

40

x2

0

10

20

30

z

40

20

0

20

40

x1

4020

0

20

40

x2

0

10

20

30zh

z



Rotating Quark in Deformed Metric Models

Vacuum radiation is independent of the deformation .

Universal scaling in the crossover regime.

40

20

0

20

40

x1

40

20

0

20

40

x2

10

20

30zh N4

zh def

z

T = 0.01, ! = 0.7, R0 = 1, " = "max

Is

then dE

dt

!

!

!

!

RotQ

!dE

dt

!

!

!

!

Drag

dE

dt

!

!

!

!

RotQ

!dE

dt

!

!

!

!

VacRad

Is

then

! ! "T, R0 ! 1/!

! ! "T, R0 ! = v " 1

Vacuum radiation of conformal N = 4

!


Although being a conjecture the AdS/CFT correspondence as a realisation of the Holographic principle is a very powerful tool for qualitative and quantitative analysis, e.g.:

Robustness and Universality of the screening distance.

Running coupling of - pairs resembles Lattice QCD data.

Robustness of the energy loss of rotating quarks in deformed models.

Many other more sophisticated models (e.g. including D3/D7 branes) available that nicely reproduce many QCD features.

Conclusions

qq


ank you for your attention!

Rotating Quark in Deformed Metric Models

Vacuum radiation is independent of the deformation

Universal scaling in the crossover regime.

40

20

0

20

40

x1

40

20

0

20

40

x2

10

20

30zh N4

zh def

z

T = 0.01, ! = 0.7, R0 = 1, " = "max

Is

then dE

dt

!

!

!

!

RotQ

!dE

dt

!

!

!

!

Drag

dE

dt

!

!

!

!

RotQ

!dE

dt

!

!

!

!

VacRad

Is

then

! ! "T, R0 ! 1/!

! ! "T, R0 ! = v " 1

Vacuum radiation of conformal N = 4

105 104 103 102 101 1 10 100

1

2

5

10

20

50

100

Γ4Ω2z2

Ωz2

v2

Ω 0.02Ω 0.2Ω 2Incoherent Sum

dE dt

! ! ! !

RotQ

"

dE dt

! ! ! !

Dra

g

dE

dt

!

!

!

!

VacRad

"

dE

dt

!

!

!

!

Drag


Metric models at finite temperature

Deformed 2-parameter metric: DeWolfe, Rosen; Gubser

5D-Einstein-Hilbert-Dilaton action:

General ansatz for metric

with parameters: c

T 2, ! !

c

"and ! =

!

3

2"z2

Temperature


Metric models at finite temperature

Deformed 2-parameter metric:

2-parameter model solves supergravity equations of motion for suitable dilaton potential V

DeWolfe, Rosen; Gubser


1 2 3 4 5 6 7 8

0.1

0.2

0.3

0.4

TTc

L!fm"

LLattice

LN!4

Screening distancein physical units

Singlet free energy from lattice (quenched) Kaczmarek, Karsch, Zantow and Petreczky, 2004


-free energy: computationGeneral formulation of the free energy:

e string action reads:

Compute drag solution for a moving heavy quark:

Final equation for the free energy

QQ

qq


Different orientation angles


Horizon function


Heavy baryon screeningConsider baryon configuration with quarks arranged on a circle

Introduce density of quarks along the circle

Nc


Baryon string configuration

We can find a stable and unstable solution. e stable one is plotted.

0.2

0.0

0.2

x30.2

0.0

0.2

x1

0

5

10


Screening distance bound for baryons

N = 4LmaxAgain is minimal for

0 1 2 3 4 50.26

0.27

0.28

0.29

0.30

0.31

0.32

0.33

!

"Tcosh!!"L m

ax

2#param. String

2#param. Einstein

SWT

N $ 4


Free energy for baryons



Radial function of the rotating quark. e dots denote the point where the string reaches the local speed of light in the bulk.

0

1

2

3

4

5

6

7

4 5 6 7 8 9

z

R!z"

T ! 0.15T ! 0.1T ! 0.09T ! 0.07T ! 0.05T ! 0

T 0


Applications of Holography in Hot Strongly Coupled Plasmas · Condensed Matter Physics...

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