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
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.
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)
Holography, Gauge/Gravity duals, AdS/CFT correspondence, ...
...many realisations, but one concept.
MPI, November 18, 2011- Seminar 2011
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.
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)
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
PHYSICAL REVIEW D 83, 066004 (2011)
Holography, Gauge/Gravity duals, AdS/CFT correspondence, ...
...many realisations, but one concept.
MPI, November 18, 2011- Seminar 2011
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.
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)
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
PHYSICAL REVIEW D 83, 066004 (2011)
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
PHYSICAL REVIEW D 81, 115004 (2010)
Holography, Gauge/Gravity duals, AdS/CFT correspondence, ...
...many realisations, but one concept.
MPI, November 18, 2011- Seminar 2011
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
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
!/ssimilar
O‘H
ara e
t al.,
2002
ALICE, 2010 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
!/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
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
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
MPI, November 18, 2011- Seminar 2011
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
MPI, November 18, 2011- Seminar 2011
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
MPI, November 18, 2011- Seminar 2011
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!)
MPI, November 18, 2011- Seminar 2011
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
MPI, November 18, 2011- Seminar 2011
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
MPI, November 18, 2011- Seminar 2011
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
MPI, November 18, 2011- Seminar 2011
Screening distance in hot moving plasmas
Nambu-Goto action:
with
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
MPI, November 18, 2011- Seminar 2011
Screening distance in hot moving plasmasStatic - pair in a hot moving plasma “wind” blowing in -direction
Nambu-Goto action:
with
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
velocity
orientation angle
v = tanh !
!
x2
v
v
MPI, November 18, 2011- Seminar 2011
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
MPI, November 18, 2011- Seminar 2011
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
MPI, November 18, 2011- Seminar 2011
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
MPI, November 18, 2011- Seminar 2011
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.
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
MPI, November 18, 2011- Seminar 2011
Coupling is defined as in QCD.
Many possibilities by rescaling the parameters.
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
MPI, November 18, 2011- Seminar 2011
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
MPI, November 18, 2011- Seminar 2011
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
MPI, November 18, 2011- Seminar 2011
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
MPI, November 18, 2011- Seminar 2011
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 at Finite Temperature
MPI, November 18, 2011- Seminar 2011
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
!
MPI, November 18, 2011- Seminar 2011
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
MPI, November 18, 2011- Seminar 2011
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
MPI, November 18, 2011- Seminar 2011
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
MPI, November 18, 2011- Seminar 2011
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
MPI, November 18, 2011- Seminar 2011
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
MPI, November 18, 2011- Seminar 2011
-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
MPI, November 18, 2011- Seminar 2011
Different orientation angles
MPI, November 18, 2011- Seminar 2011
Horizon function
MPI, November 18, 2011- Seminar 2011
Heavy baryon screeningConsider baryon configuration with quarks arranged on a circle
Introduce density of quarks along the circle
Nc
MPI, November 18, 2011- Seminar 2011
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
MPI, November 18, 2011- Seminar 2011
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
MPI, November 18, 2011- Seminar 2011
Free energy for baryons
MPI, November 18, 2011- Seminar 2011
Rotating Quark at Finite Temperature
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
MPI, November 18, 2011- Seminar 2011