equation of state and phase diagram of strongly interacting ...pawlowsk/talks/qm14...full dynamical...
TRANSCRIPT
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Equation of state and phase diagram of
strongly interacting matter
Jan M. Pawlowski
Universität Heidelberg & ExtreMe Matter Institute
Darmstadt, May 22 2014th
1
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C. Fischer ‘Locating the CEP’
A. Tripolt ‘Spectral functions from the functional renormalization group’
N. Strodthoff ‘QCD-like theories at finite density’
M. Mitter ‘Phase Structure of Strongly Interacting Matter: Thermodynamics and Chiral Anomaly’
R. Stiele ‘Thermodynamics and phase structure of strongly-interacting matter’
K. Morita ‘The Chiral Criticality in the Probability Distribution of Conserved Charges’
Related Talks & Posters
L. Fister ‘On the phase structure and dynamics of QCD’
M. Huber ‘Nonperturbative gluonic three-point correlations’
M. Hopfer ‘The role of the quark-gluon vertex function in the QCD phase transition’
M. Strickland ‘Three loop HTL perturbation theory at finite temperature and chemical potential’
2
https://indico.cern.ch/event/219436/session/11/contribution/95https://indico.cern.ch/event/219436/session/11/contribution/95https://indico.cern.ch/event/219436/session/11/contribution/378https://indico.cern.ch/event/219436/session/11/contribution/378https://indico.cern.ch/event/219436/session/2/contribution/438https://indico.cern.ch/event/219436/session/2/contribution/438https://indico.cern.ch/event/219436/session/2/contribution/463https://indico.cern.ch/event/219436/session/2/contribution/463https://indico.cern.ch/event/219436/session/2/contribution/627https://indico.cern.ch/event/219436/session/2/contribution/627https://indico.cern.ch/event/219436/session/2/contribution/590https://indico.cern.ch/event/219436/session/2/contribution/590https://indico.cern.ch/event/219436/session/2/contribution/581https://indico.cern.ch/event/219436/session/2/contribution/581https://indico.cern.ch/event/219436/session/2/contribution/173https://indico.cern.ch/event/219436/session/2/contribution/173https://indico.cern.ch/event/219436/session/2/contribution/398https://indico.cern.ch/event/219436/session/2/contribution/398https://indico.cern.ch/event/219436/session/18/contribution/21https://indico.cern.ch/event/219436/session/18/contribution/21
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Tem
per
atu
re
µ
early universe
neutron star cores
LHCRHIC
SIS
AGS
quark−gluon plasma
hadronic fluid
nuclear mattervacuum
FAIR/JINR
SPS
n = 0 n > 0
∼ 0
= 0/
= 0/
phases ?
quark matter
crossover
CFLB B
superfluid/superconducting
2SC
crossover
3
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!Phase Structure of QCD and Equation of State
!Spectral Functions & Transport Coefficients
!Outlook
Outline
4
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Functional Methods for QCD
hq(x1) · · · q̄(x2n)Aµ(y1) · · ·Aµ(ym)i
quark-gluon correlations -1 -1 -1-1
5
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Functional Methods for QCD
quark-gluon-hadron correlations -1 -1 -1-1hq(x1) · · · q̄(x2n)Aµ(y1) · · ·Aµ(ym)h(z1) · · ·h(zl)i
5
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Functional Methods for QCD
Functional renormalisation group equations
Dyson-Schwinger equations
2PI/nPI hierarchies
...
Xoff-shell
off-shell(
functional relations
' +... ... ... ... ...scattering amplitude/vertex functions
(
quark-gluon-hadron correlations -1 -1 -1-1hq(x1) · · · q̄(x2n)Aµ(y1) · · ·Aµ(ym)h(z1) · · ·h(zl)i
5
-
Functional Methods for QCD
Xoff-shell
off-shell(
functional relations
' +... ... ... ... ...scattering amplitude/vertex functions
(
properties
access to physics mechanisms
low energy models naturally encorporated
numerically tractable no sign problemsystematic error control via closed form
lattice: see talk of D. Sexty
quark-gluon-hadron correlations -1 -1 -1-1hq(x1) · · · q̄(x2n)Aµ(y1) · · ·Aµ(ym)h(z1) · · ·h(zl)i
5
-
Functional Methods for QCD
Xoff-shell
off-shell(
functional relations
' +... ... ... ... ...scattering amplitude/vertex functions
(
properties
access to physics mechanisms
low energy models naturally encorporated
numerically tractable no sign problemsystematic error control via closed form
lattice: see talk of D. Sexty
QCD low energy models
quark-gluon-hadron correlations -1 -1 -1-1hq(x1) · · · q̄(x2n)Aµ(y1) · · ·Aµ(ym)h(z1) · · ·h(zl)i
5
-
Functional Methods for QCD
Xoff-shell
off-shell(
functional relations
' +... ... ... ... ...scattering amplitude/vertex functions
(
properties
access to physics mechanisms
low energy models naturally encorporated
numerically tractable no sign problemsystematic error control via closed form
lattice: see talk of D. Sexty
QCD low energy models
quark-gluon-hadron correlations -1 -1 -1-1hq(x1) · · · q̄(x2n)Aµ(y1) · · ·Aµ(ym)h(z1) · · ·h(zl)i
e.g. lattice input on rhs
FunMethods complementary to lattice
e.g. volume flucs., finite density, dynamics, ...
5
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Functional Methods for QCDFunctional RG
@t�k[�] =
free energy/grand potential
gluequantum fluctuations
quark quantum fluctuations
hadronic quantum fluctuations
! "#$ S"#$ !k
k=%
k
"#$
k 0
IR UV
k- k&
RG-scale k: t = ln k
free energy at momentum scale k
JMP, AIP Conf.Proc. 1343 (2011)
FRG QCD surveyJMP, Aussois ’12
Phase diagram surveyJMP, Schladming ’13
6
http://www.thphys.uni-heidelberg.de/~pawlowsk/talks/schladming13_pawlowski.pdfhttp://www.thphys.uni-heidelberg.de/~pawlowsk/talks/schladming13_pawlowski.pdfhttp://www.thphys.uni-heidelberg.de/~pawlowsk/talks/erg12_pawlowski.pdfhttp://www.thphys.uni-heidelberg.de/~pawlowsk/talks/erg12_pawlowski.pdf
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Functional Methods for QCDFunctional RG
@t�k[�] =
free energy/grand potential
gluequantum fluctuations
quark quantum fluctuations
hadronic quantum fluctuations
! "#$ S"#$ !k
k=%
k
"#$
k 0
IR UV
k- k&
RG-scale k: t = ln k
free energy at momentum scale k
JMP, AIP Conf.Proc. 1343 (2011)
FRG QCD surveyJMP, Aussois ’12
Phase diagram surveyJMP, Schladming ’13
dynamical Gies, Wetterich ’01 JMP ’05 Flörchinger, Wetterich ’09
Dynamical hadronisation
· · ·
6
http://www.thphys.uni-heidelberg.de/~pawlowsk/talks/schladming13_pawlowski.pdfhttp://www.thphys.uni-heidelberg.de/~pawlowsk/talks/schladming13_pawlowski.pdfhttp://www.thphys.uni-heidelberg.de/~pawlowsk/talks/erg12_pawlowski.pdfhttp://www.thphys.uni-heidelberg.de/~pawlowsk/talks/erg12_pawlowski.pdf
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Functional Methods for QCD
∂t = 2 + + +2
@t = � 3 +6 +3 � 6
� 12
+
∂t−1
= +
∂t−1
= − −1/2
+
2PI-resummation
DSE-flowYang-Mills propagators
2
3
4
1
0 5 64321
FRG: Fischer, Maas, JMP, Annals Phys. 324 (2009) 2408
lattice: Sternbeck et al, PoS LAT2006 (2006) 076
p2�A A⇥(p2)
p [GeV]
Yang-Mills
... +
see poster of M. Huber
7
-
QCD
@t�k[�] =
0
5
10
15
20
25
30
35
0.1 1 10
Yuka
wa
inte
ract
ion
h(k
)
k [GeV]
FRG-QCD: Fister, Herbst, Mitter, Rennecke, Strodthoff, JMP
preliminary
quark-meson coupling
hk
90
8
-
QCD
@t�k[�] =
0
5
10
15
20
25
30
35
0.1 1 10
Yuka
wa
inte
ract
ion
h(k
)
k [GeV]
FRG-QCD: Fister, Herbst, Mitter, Rennecke, Strodthoff, JMP
preliminary
quark-meson coupling
hk
Low energy models
FRG:
(com
plet
ely)
fixe
d fro
m Q
CD
Model results on the phase structure of QCD
∂tΓk[φ] =1
2− − + 1
2+ ∂tΓk[φ] = 12 − − + 12+
PQM-model PNJL-model QM-model NJL-model
90
8
-
Functional Methods for QCD
- + 12
present best approximation
∂t−1
= +
∂t−1
= − −1/2
+
momentum dependence
∂t = 2 + + +2
@t = � 3 +6 +3 � 6
� 12
+
momentum dependence
2PI-resummed momentum dependence
�
momentum dependence
momentum dependence
+matter-contributions
all tensor structures
h[⇥,⇤�]
full mesonic field-dependence
momentum dependence
Aconst0
full field-dependence
+ ...
... +
Ve� [⇥,⇤�;A0]all tensor structures
FRG-QCD: Fister, Herbst, Mitter, Rennecke, Strodthoff, JMP
DSE: see poster of M. Hopfer
9
-
Phase Structure and Equation of State
10
-
Confinement
0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25
0.0
0.2
0.4
0.6
0.8
1.0
T/Tc
Polyakov loop
SU(3)
�gA02⇥
-0.5-0.4-0.3-0.2-0.1
0 0.1 0.2 0.3 0.4
0 0.2 0.4 0.6 0.8 1
!4 V
(! <"
0>)
! /(2#)
0.3 0.5 0.7
276 MeV
295 MeV
286 MeV
280 MeV
276 MeV
271 MeV
�4 VYM[A0]
Polyakov loop Potential
�[A0] =1
3
(1 + 2 cos
1
2
�gA0)
lattice : Tc/p
� = 0.646
Tc/p
� = 0.658± 0.023
�
Braun, Gies, JMP, PLB 684 (2010) 262
Fister, JMP, PRD 88 (2013) 045010
FRG:
FRG, DSE, 2PI:
see also talk of C. Sasaki
11
-
Confinement
0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25
0.0
0.2
0.4
0.6
0.8
1.0
T/Tc
Polyakov loop
SU(3)
�gA02⇥
-0.5-0.4-0.3-0.2-0.1
0 0.1 0.2 0.3 0.4
0 0.2 0.4 0.6 0.8 1
!4 V
(! <"
0>)
! /(2#)
0.3 0.5 0.7
276 MeV
295 MeV
286 MeV
280 MeV
276 MeV
271 MeV
�4 VYM[A0]
Polyakov loop Potential
�[A0] =1
3
(1 + 2 cos
1
2
�gA0)
lattice : Tc/p
� = 0.646
Tc/p
� = 0.658± 0.023
Fister, JMP, arXiv:1112.5440
0.0 0.5 1.0 1.5 2.00
1
2
3
4
5
p [GeV]
Transversal Propagator GT
FRG: T = 0
FRG: T = 0.361Tc
FRG: T = 0.903Tc
FRG: T = 1.81Tc
Lattice: T = 0
Lattice: T = 0.361Tc
Lattice: T = 0.903Tc
Lattice: T = 1.81Tc
transversal gluon propagator
gauge independence
from the full propagators
confinement criteria
�
Braun, Gies, JMP, PLB 684 (2010) 262
Fister, JMP, PRD 88 (2013) 045010
FRG:
FRG, DSE, 2PI:
see also talk of C. Sasaki
11
-
Full dynamical QCDPhase structure
Braun, Haas, Marhauser, JMP, PRL 106 (2011) 022002
0
50
100
150
200
250
300
0 π/3 2π/3 π 4π/3
T [M
eV
]
2πθ
TconfTχ
imaginary chemical potential
=2Nf
T� ' Tconf
chiral limit
0
0.2
0.4
0.6
0.8
1
150 160 170 180 190 200 210 220 230
T [MeV]
fπ(T)/fπ(0)
Dual density
Polyakov Loop
160 180 200
χL,d
ual
12
-
Full dynamical QCDPhase structure
Braun, Haas, Marhauser, JMP, PRL 106 (2011) 022002
0
50
100
150
200
250
300
0 π/3 2π/3 π 4π/3
T [M
eV
]
2πθ
TconfTχ
imaginary chemical potential
=2Nf
T� ' Tconf
chiral limit
0
0.2
0.4
0.6
0.8
1
150 160 170 180 190 200 210 220 230
T [MeV]
fπ(T)/fπ(0)
Dual density
Polyakov Loop
160 180 200
χL,d
ual
see talk of C. Fischer
Luecker, Fischer, Fister, JMP, PoS CPOD2013 (2013) 057 Fischer, Luecker, Welzbacher, arXiv:1405.4762
50 100 150 200 250T [MeV]
0
0.2
0.4
0.6
0.8
1
∆l,
s(T
)/∆
l,s(
0)
Lattice QCDQuark Condensate
=2+1Nf
0
0.2
0.4
0.6
0.8
1
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
∆l,s
t
Wuppertal-Budapest, 2010
PQM FRG
PQM eMF
PQM MF
Herbst, Mitter et al, PLB 731 (2014) 248-256
QCD-improved PQM model DSE
12
-
Glue Potential
Yang-Mills Potential
Polyakov loop potential in full QCD
0 0.2 0.4 0.6 0.8 1βgA0 / 2π
-0.8
-0.6
-0.4
-0.2
0
β4V
[A0]
glueYang-Mills
t = -0.05
t = 0
t = 0.05
�4V [A0]
JMP, AIP Conf.Proc. 1343 (2011)
Haas, Stiele et al, PRD 87 (2013) 076004
Full dynamical QCDImproving models towards QCD
U [�, �̄]
�[A0]
�gA02⇥
see poster of R. Stiele
@t�k[�] =
@t�k[�] =Yang-Mills
glue
13
-
Glue Potential
Yang-Mills Potential
Polyakov loop potential in full QCD
0 0.2 0.4 0.6 0.8 1βgA0 / 2π
-0.8
-0.6
-0.4
-0.2
0
β4V
[A0]
glueYang-Mills
t = -0.05
t = 0
t = 0.05
�4V [A0]
Full dynamical QCDImproving models towards QCD
U [�, �̄]
�[A0]
�gA02⇥
Mitter, Schaefer, Phys.Rev. D89 (2014) 054027
0
200
400
600
800
1000
1200
0 50 100 150 200 250 300
mass
es
[MeV
]
T [MeV]
π, η’σ
a0η
without anomalous breaking of axial U(1)
0
200
400
600
800
1000
1200
0 50 100 150 200 250 300
mass
es
[MeV
]
T [MeV]
π σ a0 η’ η
with anomalous breaking of axial U(1)
see poster of M. Mitter
QM-model
13
-
Full dynamical QCD
Herbst, Mitter, JMP, Schaefer, Stiele, Phys.Lett. B731 (2014) 248-256
Pressure
Shaded area: systematic error estimate due to low initial scale 1 GeV
Interaction measure
0
1
2
3
4
5
6
7
8
-0.6 -0.4 -0.2 0 0.2 0.4 0.6(ε
- 3
P)/
T4
t
Wuppertal-Budapest, 2010
HotQCD Nt=8, 2012
HotQCD Nt=12, 2012
PQM FRG
PQM eMF+π
PQM MF+π
PQM eMF
0
0.5
1
1.5
2
2.5
3
3.5
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
P/T
4
t
Wuppertal-Budapest, 2010
PQM FRG
PQM eMF+π
PQM MF+π
PQM eMF
Equation of state
see poster of M. Mitter
lattice: see talk of A. Bazavov
high T: see talk of M. Strickland
14
-
0 0.2 0.4 0.6 0.8 1βgA0 / 2π
-0.8
-0.6
-0.4
-0.2
0
β4V
[A0]
glueYang-Mills
t = -0.05
t = 0
t = 0.05
Full dynamical QCDPhase structure at finite density
0 50
100
150
200
0 50 100 150 200 250 300 350
T [
Me
V]
µ [MeV]
mπ=138 MeV
χ crossoverσ(T=0)/2Φ crossover—Φ crossoverχ 1st orderCEP
Polyakov loop potential in full QCD
FRG QCD results at finite densityHaas, Braun, JMP ’09, unpublished
Herbst, JMP, Schaefer, PLB 696 (2011) 58-67 PRD 88 (2013) 1, 014007
�4V [A0]
Phase diagram of quantised PQM-model
15
-
0 0.2 0.4 0.6 0.8 1βgA0 / 2π
-0.8
-0.6
-0.4
-0.2
0
β4V
[A0]
glueYang-Mills
t = -0.05
t = 0
t = 0.05
Full dynamical QCDPhase structure at finite density
0 50
100
150
200
0 50 100 150 200 250 300 350
T [
Me
V]
µ [MeV]
mπ=138 MeV
χ crossoverσ(T=0)/2Φ crossover—Φ crossoverχ 1st orderCEP
Polyakov loop potential in full QCD
�4V [A0]
Phase diagram of quantised PQM-model µBT
= 2
see poster of N. Strodthoff
diquarks, baryons,
see poster of K. Morita
higher moments
inhomogeneous phases
0
50
100
150
200
0 100 200 300 400 500
T[M
eV]
µ [MeV]
Chiral density wavehom. spinodalshom. 1st orderhom. 2nd order
Müller, Buballa, Wambach, PLB 727 (2013) 240 Carignano, Buballa, Schaefer, arXiv:1404.0057
0
30
60
90
120
150
180
0 50 100 150 200 250 300 350 400 450
T (M
eV)
µ (MeV)
15
-
µBT
= 3
Full dynamical QCDPhase structure at finite density
Phase diagram of quantised PQM-model
0
50
100
150
200
0 50 100 150 200 250 300 350
T [
Me
V]
µ [MeV]
mπ=138 MeV
χ crossoverσ(T=0)/2Φ crossover—Φ crossoverχ 1st orderCEP
Phase diagram of 2+1 flavor QCD
DSE
Polyakov loop at finite density
0 50 100 150 200µq [MeV]
0
50
100
150
200
T [M
eV]
Lattice: curvature range κ=0.0066-0.0180DSE: chiral crossoverDSE: critical end pointDSE: deconfinement crossover
µB/T=2µB/T=3
lattice curvature
µBT
< 2
Critical point unlikely for
µBT
= 2
see talk of C. Fischer
Fischer, Luecker, PLB 718 (2013) 1036
Fischer, Fister, Luecker, JMP, PLB732 (2014) 248
Kaczmarek at al. ’11Endrodi, Fodor, Katz, Szabo ’11Cea, Cosmai, Papa ’14
16
-
µBT
= 3
Full dynamical QCDPhase structure at finite density
Phase diagram of quantised PQM-model
0
50
100
150
200
0 50 100 150 200 250 300 350
T [
Me
V]
µ [MeV]
mπ=138 MeV
χ crossoverσ(T=0)/2Φ crossover—Φ crossoverχ 1st orderCEP
Phase diagram of 2+1 flavor QCD
DSE
Polyakov loop at finite density
0 50 100 150 200µq [MeV]
0
50
100
150
200
T [M
eV]
Lattice: curvature range κ=0.0066-0.0180DSE: chiral crossoverDSE: critical end pointDSE: deconfinement crossover
µB/T=2µB/T=3
lattice curvature
µBT
< 2
Critical point unlikely for
µBT
= 2
16
-
Spectral functions & Transport Coefficients
17
-
Viscosity in pure glue
Complex DSEs
Tripolt, Strodthoff, von Smekal, Wamach, PRD 89 (2014) 034010 Kamikado, Strodthoff, von Smekal, Wambach, EPJ C74 (2014) 2806
spectral functions
T=100
FRG
gluon spectral function
T=100 MeV - 1 GeVT=0
analytic complex FRG
M. Haas, Fister, JMP, arXiv:1308.4960
FRG+MEM
Strauss, Fischer, Kellermann, PRL 109 (2012) 252001
pion and sigma spectral functions
see talk of A. Tripolt
see poster of L. Fister
18
-
Viscosity in pure glue
pure glue
PHSD spectral functions
T=1.44 Tc
=2+1Nf
spectral functions
T=1.44 Tc
transversalM. Haas, Fister, JMP, arXiv:1308.4960
see talk of E. Bratkovskaya
see poster of L. Fister
19
-
Viscosity in pure glueshear viscosity
T . 2Tc
Shaded area: MEM error estimates
: MEM+optimised RG-scheme systematic error estimates
M. Haas, Fister, JMP, arXiv:1308.4960
H. Meyer ’09
entropy lattice
Kubo relation
Diagrammatic representation
=⇢⇡⇡ + +
+ ... 3-loop closed form
⌘ =1
20
d
d!
����!=0
⇢⇡⇡(!, 0)
H. Meyer ’09
20
-
Viscosity in pure glueshear viscosity
T . 2Tc
Shaded area: MEM error estimates
: MEM+optimised RG-scheme systematic error estimates
minimum at T = 1.25 : Tc⌘
s= 1.45
1
4⇡
scale matching with QCD: ⌘
s= 2.27
1
4⇡
M. Haas, Fister, JMP, arXiv:1308.4960
20
-
Viscosity in pure glueshear viscosity
minimum at T = 1.25 : Tc⌘
s= 1.45
1
4⇡
scale matching with QCD: ⌘
s= 2.27
1
4⇡
Christiansen, M. Haas, JMP, Strodthoff, in prep.
2-loop terms
21
-
Viscosity in pure glueshear viscosity
minimum at T = 1.25 : Tc⌘
s= 1.45
1
4⇡
scale matching with QCD: ⌘
s= 2.27
1
4⇡
Christiansen, M. Haas, JMP, Strodthoff, in prep.
Chen, Deng, Dong, Wang ’11
Yang-Mills
2-loop terms
21
-
Viscosity in pure glueshear viscosity
minimum at T = 1.25 : Tc⌘
s= 1.45
1
4⇡
scale matching with QCD: ⌘
s= 2.27
1
4⇡
Christiansen, M. Haas, JMP, Strodthoff, in prep.
Chen, Deng, Dong, Wang ’11
Yang-Mills
Chen, Deng, Dong, Wang ’11
scale matching
2-loop terms
21
-
Summary & Outlook
22
-
!Phase structure and Equation of State
Summary & outlook
0
0.5
1
1.5
2
2.5
3
3.5
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
P/T
4
t
Wuppertal-Budapest, 2010
PQM FRG
PQM eMF
PQM MF
0 50 100 150 200µq [MeV]
0
50
100
150
200
T [M
eV]
Lattice: curvature range κ=0.0066-0.0180DSE: chiral crossoverDSE: critical end pointDSE: deconfinement crossover
µB/T=2µB/T=3
0
50
100
150
200
250
300
0 π/3 2π/3 π 4π/3
T [
Me
V]
2πθ
TconfTχ
µBT
= 3
0
50
100
150
200
0 50 100 150 200 250 300 350
T [M
eV
]
µ [MeV]
mπ=138 MeV
χ crossoverσ(T=0)/2Φ crossover—Φ crossoverχ 1st orderCEP
µBT
= 2
0
1
2
3
4
5
6
7
8
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
(ε -
3P
)/T
4
t
Wuppertal-Budapest, 2010
HotQCD Nt=8, 2012
HotQCD Nt=12, 2012
PQM FRG
PQM eMF+π
PQM MF+π
PQM eMF
23
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!Phase structure and Equation of State
!Spectral functions and Transport Coefficients
Summary & outlook
24
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!Phase structure and Equation of State
!Spectral functions and Transport Coefficients
!Towards quantitative precision
!Baryons, high density regime, dynamics
!Hadronic properties
!hadron spectrum & in medium modifications
! low energy constants
Summary & outlook
25