Heavy Probes in Strongly Coupled Plasmas
With Chemical Potential
Andreas Samberg
in collaboration with Carlo Ewerz
Institut für Theoretische Physik
Universität Heidelberg
July 25, Karl Schwarzschild Meeting 2013, Frankfurt
Andreas Samberg (Heidelberg U)
Heavy Probes in Strongly Coup. Plasmas With Chem. Pot.
KSM 2013
Outline
1
Introduction
Motivation
Holography
Quark-Gluon Plasma
2
Applications to Strongly Coupled Plasmas
Color Screening
Q Q̄ Free Energy & Running Coupling
3
Conclusion
Andreas Samberg (Heidelberg U)
Heavy Probes in Strongly Coup. Plasmas With Chem. Pot.
KSM 2013
Introduction
Motivation
GSI, Darmstadt
Strong Coupling and Finite Chemical Potential
Sketch of QCD phase diagram.
Andreas Samberg (Heidelberg U)
RHIC & LHC: Quark-gluon
plasma at T & Tc strongly
coupled fluid
Gauge/gravity duality as
non-perturbative approach
Include nonzero chemical
potential
Heavy Probes in Strongly Coup. Plasmas With Chem. Pot.
KSM 2013
Introduction
Holography
Maldacena, 2003
Holographic Principle
Concrete realization:
[Maldacena, Gubser, Klebanov, Polyakov, Witten, 1997/98]
N = 4 super Yang-Mills
Andreas Samberg (Heidelberg U)
←→
Type IIB string theory on
AdS5 × S 5
Heavy Probes in Strongly Coup. Plasmas With Chem. Pot.
KSM 2013
Introduction
Holography
AdS/CFT Correspondence
AdS5 : 5-dim. spacetime, negative curvature
ds 2 =
boundary
R2
2
2
2
−dt
+
d~
x
+
dz
z2
z
R 1,3
bulk
(strings
live here)
Andreas Samberg (Heidelberg U)
Heavy Probes in Strongly Coup. Plasmas With Chem. Pot.
KSM 2013
Introduction
Holography
AdS/CFT Correspondence
AdS5 -BH: 5-dim. spacetime, negative curvature with black hole
R2
1
2
2
2
2
ds = 2 −h(z)dt + d~x +
dz
z
h(z)
boundary
z
Temperature:
T > 0 ←→ Black hole
T ∼ zh−1
R 1,3
bulk
(strings
live here)
horizon
Andreas Samberg (Heidelberg U)
zh
Heavy Probes in Strongly Coup. Plasmas With Chem. Pot.
KSM 2013
Introduction
Holography
AdS/CFT Correspondence
AdS5 -BH: 5-dim. spacetime, negative curvature with black hole
R2
1
2
2
2
2
ds = 2 −h(z)dt + d~x +
dz
z
h(z)
boundary
z
Temperature:
T > 0 ←→ Black hole
T ∼ zh−1
R 1,3
bulk
(strings
live here)
Chemical potential:
µ > 0 ←→ Charged BH
µ∼Q
Q
horizon
Andreas Samberg (Heidelberg U)
zh
Heavy Probes in Strongly Coup. Plasmas With Chem. Pot.
KSM 2013
Introduction
Holography
Strong/Weak Duality
The AdS/CFT duality is strong ←→ weak
Number of colors Nc → ∞
←→
’t Hooft coupling λ → ∞
←→
gs → 0
Strings behave classically
α0 L2AdS
Strings behave pointlike
In limit of many colors & strong coupling:
Strongly coupled QFT ←→ Classical (super-)gravity
Andreas Samberg (Heidelberg U)
Heavy Probes in Strongly Coup. Plasmas With Chem. Pot.
KSM 2013
Introduction
Quark-Gluon Plasma
© C. Ewerz, K. Schade, EMMI; Different Arts 2011
Ewerz, Schade,
Different Arts, 2011
Heavy Ion Collisions: Quark-Gluon Plasma
RHIC & LHC: QGP strongly coupled ⇒ Apply duality
Thermodynamics: Energy density , pressure p, − 3p, etc.
Transport coefficients: Shear viscosity, bulk viscosity, etc.
Famous conjecture:
η
1
≥
s
4π
for all physical substances
[Kovtun, Son, Starinets, 2005]
Jet quenching, parton energy loss (drag force)
Color screening, quark–antiquark free energy, running coupling
Andreas Samberg (Heidelberg U)
Heavy Probes in Strongly Coup. Plasmas With Chem. Pot.
KSM 2013
Applications to Strongly Coupled Plasmas
Apply AdS/CFT to QCD?
In vacuum, N = 4 SYM very different from QCD:
Maximally supersymmetric
Conformal, constant coupling
No confinement, no chiral symmetry breaking
Nc → ∞ for the duality
But, at finite temperature T , differences are smaller:
Above 2Tc , QCD closer to conformal
No confinement in QCD above Tc
Finite T breaks supersymmetry in N = 4 SYM
Also, we can go away from N = 4 SYM
‘Bottom-up’ approach
We work on the gravity side (5D) of the duality and deform the AdS space,
breaking conformal invariance in the dual field theory.
Andreas Samberg (Heidelberg U)
Heavy Probes in Strongly Coup. Plasmas With Chem. Pot.
KSM 2013
Applications to Strongly Coupled Plasmas
Our Rationale
One way: Try to mimic QCD.
Difficult, as one does not exactly know what one is doing on the field
theory side.
Other way: Try to find universal features of strongly coupled systems
by considering classes of theories.
For example:
KSS bound on η/s
Screening distance conjecture and proof by Ewerz, Schade
Andreas Samberg (Heidelberg U)
Heavy Probes in Strongly Coup. Plasmas With Chem. Pot.
KSM 2013
Applications to Strongly Coupled Plasmas
Simple Models
at Finite Temperature and Chemical Potential
Conformal: AdS-Reissner–Nordström ←→ N = 4 SYM
R2
1
2
2
2
2
ds = 2 −h(z)dt + d~x +
dz
z
h(z)
µ2 zh2 z 4 µ2 zh2 z 6
+
h(z) = 1 − 1 +
3
3 zh6
zh4
Non-conformal: CGN model metric [Colangelo, Giannuzzi, Nicotri, 2010]
2
1
2
c 2z 2 R
2
2
2
ds = e
−h(z)dt + d~x +
dz
z2
h(z)
Ad hoc deformation (‘soft wall’) due to scale c
Has its shortcomings at low µ and/or T
Andreas Samberg (Heidelberg U)
Heavy Probes in Strongly Coup. Plasmas With Chem. Pot.
KSM 2013
Applications to Strongly Coupled Plasmas
More Sophisticated Models
Non-conformal: 1-parameter models
Action
[DeWolfe, Gubser, Rosen, 2010]
S=
1
2κ2
Z
√
d5 x −G
f (φ)
1
Fµν F µν
R − ∂µ φ∂ µ φ − V (φ) −
2
4
Solve with ansatz
e2B(z) 2
ds 2 = e2A(z) −h(z)dt 2 + d~x 2 +
dz
h(z)
r
R
3 2
A(z) = log
and φ(z) =
κz
z
2
Solves 5d gravity action: Consistent deformation due to scale κ
Evades problems of CGN model at low µ/T
Andreas Samberg (Heidelberg U)
Heavy Probes in Strongly Coup. Plasmas With Chem. Pot.
KSM 2013
Applications to Strongly Coupled Plasmas
Color Screening
Screening Distance
Consider heavy, moving Q Q̄ pair
L
Q
Q̄
z
~v
No bound states if separation too large
Q Q̄ pair ←→ endpoints of string
Nambu–Goto action
Z
p
SNG = d2 σ − det gab
String configuration from classical
condition
charged BH
zh
!
0 = δSNG
Free energy from extremal SNG
Andreas Samberg (Heidelberg U)
Heavy Probes in Strongly Coup. Plasmas With Chem. Pot.
KSM 2013
Applications to Strongly Coupled Plasmas
Color Screening
Screening Distance
For L < Ls one stable string
configuration
For L > Ls no Q Q̄ bound state
Ls is the screening distance
Universal behavior at µ = 0:
N =4 SYM
Ldef
s > Ls
for consistent deformations
[Ewerz,
Schade]
Andreas Samberg (Heidelberg U)
Heavy Probes in Strongly Coup. Plasmas With Chem. Pot.
KSM 2013
Applications to Strongly Coupled Plasmas
Color Screening
Screening Distance in (µ, T ) Plane
(1-parameter model (φ as dilaton), ~
v = 0)
Andreas Samberg (Heidelberg U)
Heavy Probes in Strongly Coup. Plasmas With Chem. Pot.
KSM 2013
Applications to Strongly Coupled Plasmas
Color Screening
Screening Distance in (µ, T ) Plane
0.90
Μ = 3.5, T = 1
0.85
ΠLs T cosh12 Η
AdS-RN
ΚEinstein = 7
0.80
max
ΚEinstein
= 15.5
0.75
0.70
Κstring
=7
max
Κstring
= 15.5
0.65
0.60
0.55
0
1
2
3
4
Η
(Velocity-dependence of Ls in 1-parameter models)
(1-parameter model (φ as dilaton), ~
v = 0)
At suff. large µ and/or velocity: Screening distance in conformal
theory no longer lower bound
But: Deviations from lower bound small (robustness)
Andreas Samberg (Heidelberg U)
Heavy Probes in Strongly Coup. Plasmas With Chem. Pot.
KSM 2013
Applications to Strongly Coupled Plasmas
Color Screening
Screening Distance—Ultrarelativistic Behavior
0.90
Μ = 3.5 , T = 1
ΠLs T cosh 12 Η
0.85
AdS-RN
Κ = 3 Einstein
Κ = 3 string
Κ = 7 Einstein
Κ = 7 string
Κ = 15.5 Einstein
Κ = 15.5 string
0.80
0.75
0.70
0.65
0.60
0.55
0
1
2
3
4
5
6
Η
(Velocity-dependence of Ls in 1-parameter models)
Faster velocity lowers screening distance with scaling law
√
∝ 1/ γ ∝ (boosted energy dens.)−1/4
contradicts expectation from [Caceres, Natsuume, Okamura, ’06]
Andreas Samberg (Heidelberg U)
Heavy Probes in Strongly Coup. Plasmas With Chem. Pot.
KSM 2013
Applications to Strongly Coupled Plasmas
Q Q̄ Free Energy & Running Coupling
Free Energy & Running Coupling αQ Q̄
0
E T -1 Λ-12
-2
̐ T
̐ T
̐ T
̐ T
-4
-6
-8
0.00
0.05
0.10
0.15
0.20
=0
=1
=5
= 10
0.25
0.30
LT
(N = 4 SYM, ~
v = 0)
Increasing µ lowers binding energy
Andreas Samberg (Heidelberg U)
Heavy Probes in Strongly Coup. Plasmas With Chem. Pot.
KSM 2013
Applications to Strongly Coupled Plasmas
Q Q̄ Free Energy & Running Coupling
Free Energy & Running Coupling αQ Q̄
0
E T -1 Λ-12
-2
̐ T
̐ T
̐ T
̐ T
-4
-6
-8
0.00
0.05
0.10
0.15
0.20
=0
=1
=5
= 10
0.25
0.30
LT
(N = 4 SYM, ~
v = 0)
Increasing µ lowers binding energy
Expectation for conformal theory: E (L) ∝ −α/L
Define coupling αQ Q̄ (L) ≡ 34 L2 dEdL(L) as in lattice QCD
Andreas Samberg (Heidelberg U)
Heavy Probes in Strongly Coup. Plasmas With Chem. Pot.
KSM 2013
Applications to Strongly Coupled Plasmas
Q Q̄ Free Energy & Running Coupling
Running Coupling αQ Q̄
µ/T = 0
µ/T = 4
œ
0.25
0.20
œ
œ
0.15
̐T =0
0.16
Λ-12 ΑQ Q
Λ-12 ΑQ Q
0.18
œ
0.20
œ
œ
N = 4 SYM
Κ ’T =1
0.10
0.12
N = 4 SYM
Κ ’T =1
Κ ’T =2
0.10
Κ ’T =2
Κ ’ T = 2.4
œ
œ
̐T =4
0.14
Κ ’ T = 2.4
0.08
0.06
0.10
0.15
0.20
0.30
0.10
LT
0.15
0.20
0.30
LT
(1-parameter model (φ as dilaton))
At vanishing chemical potential µ = 0:
[Ewerz, Schade]
Thermal scale Lth ∼ 1/T sets fall-off scale
Restoration of conformality in UV: αQ Q̄ (L → 0) → const
Agrees with lattice QCD at least qualitatively
We find at finite chemical potential µ > 0:
Scale Lth depends only weakly on µ
Universal rise above UV value in all non-conformal models
Andreas Samberg (Heidelberg U)
Heavy Probes in Strongly Coup. Plasmas With Chem. Pot.
KSM 2013
Conclusion
Summary
Using gauge/gravity duality one can tackle strongly coupled problems
in QFTs.
We apply it to classes of hot strongly coupled plasmas at finite
chemical potential, and for moving probes.
We find:
Screening distance at µ = 0 has lower bound
Lower bound no longer holds at µ > 0, but screening distance and free
energy are robust observables
Running coupling αQ Q̄ (L) shows universal rise above conformal value
(Can also apply this to other observables: Drag force; jet quenching
parameter q̂, quark on circular orbit)
Andreas Samberg (Heidelberg U)
Heavy Probes in Strongly Coup. Plasmas With Chem. Pot.
KSM 2013
Conclusion
Summary
Using gauge/gravity duality one can tackle strongly coupled problems
in QFTs.
We apply it to classes of hot strongly coupled plasmas at finite
chemical potential, and for moving probes.
We find:
Screening distance at µ = 0 has lower bound
Lower bound no longer holds at µ > 0, but screening distance and free
energy are robust observables
Running coupling αQ Q̄ (L) shows universal rise above conformal value
(Can also apply this to other observables: Drag force; jet quenching
parameter q̂, quark on circular orbit)
Thank you!
Andreas Samberg (Heidelberg U)
Heavy Probes in Strongly Coup. Plasmas With Chem. Pot.
KSM 2013