phases diagram in a refined holographic qcd model
DESCRIPTION
Phases Diagram in a Refined Holographic QCD Model. Yi Yang@NCTU. May 7, 2014. XS2014 安徽 黃 山. Content. Phases in QCD Holographic QCD A M odel Summary. RHIC&LHC. Phases in QCD. χ S deconfinment. crossover. T. 1st order. χ SB confinment. CFL/CSC. μ. Critical Point. - PowerPoint PPT PresentationTRANSCRIPT
Phases Diagram in a Refined Holographic QCD Model
Yi Yang@NCTU
May 7, 2014
XS2014 安徽黃山
Content
• Phases in QCD
• Holographic QCD
• A Model
• Summary
Phases in QCD
T
μ
χSB confinment
χS deconfinment
1st order
crossover
CFL/CSC
RHIC&LHC
Critical Point
Holographic Principle
AdS/CFT
• IIB in SYM on
• Holographic duality
• Strong/weak duality
• Low energy gravity/gauge
Maldacena, Witten, Polyakov…
Holographic QCD
• Deformed AdS/QCD duality
• Top-down:
• Bottom-up: hard wall, soft wall
T
μ
χS
χSB
χSB
vacuum nuclear matter
QGP
meson quark matter
quarkmatter
Top-Down: D3-D5/D7Karch, Katz…
Top-Down: D4-D8
T
μ
χS
χSB
confinement
deconfinement
deconfinement
χSB
Sakai, Sugimoto…
Bottom-Up: Einstein-Scalar
06.2
606.0
b
𝑆𝑔=∫𝑑5𝑥 √−𝑔 [𝑅−12𝜕𝜙𝜕𝜙−𝑉 (𝜙 )]
Gubser, Nellore…𝑉 (𝜙 )=−12cosh (𝛾 𝜙 ) −𝑏𝜙2
Bottom-Up:Einstein-Maxwell-Dilaton DeWolfe, Gubser, Rosen…
𝑆𝑔=∫𝑑5𝑥 √−𝑔 [𝑅−𝑓 (𝜙 )
4𝐹2 −
12𝜕𝜙𝜕𝜙−𝑉 (𝜙)]
Potential Reconstruction
𝑆𝑔=∫𝑑5𝑥 𝑒− 2𝜙√−𝑔 [𝑅+4𝜕𝜙 𝜕𝜙−𝑉 (𝜙 )] Danning Li , Song He , Mei Huang, Qi-Shu Yan…
Potential Reconstruction RG Cai, Song He, Danning Li…𝑆𝑔=∫𝑑5𝑥 √−𝑔 [𝑅−
14𝐹 2−
12𝜕𝜙𝜕𝜙−𝑉 (𝜙)]
Linear Meson Spectrum
Soft-Wall Model
𝑚2=4𝑛+4𝑆𝑚=−14∫ 𝑑5𝑥 𝑒−𝜙√−𝑔𝐹 2→
Karch, Katz, Son, Stephanov…
Dynamical Soft-Wall Model Batell, Gherghetta; Paula, Frederico, Beyer…
A Refined AdS/QCD Model Song He, Shang-Yu Wu, Yi Yang, Pei-Hung Yuan…
𝑔=𝑒2 𝐴( 𝑧 )
𝑧 2 (−𝑔 (𝑧)𝑑 𝑡2+ 𝑑𝑧 2
𝑔(𝑧 )+𝑑 �⃗�2)
Equations of motion
𝜙 , 𝐴𝑡 ,𝑔 ,𝑉 :(𝐴 , 𝑓 )
Boundary Conditions and Constrains
• At horizon:
• At boundary:
• Linear Regge spectrum:
𝐴𝑡 (1 )=𝑔 (1 )=0
𝐴 (0 )=0 ,𝑔 (0 )=1
𝑓 (𝑧 )=𝑒±𝑐 𝑧 2 − 𝐴( 𝑧 )
Analytic Solutions
g
g
zg
g
zA
zg
gAAgezzV
zIzzIzzI
zIzI
e
c
zIzg
ze
c
e
eezA
zAAAz
A
HH
HH
czH
czcz
czcz
t
H
HH
H
6
''4
2
'31'
6
2
'3'3''3)(
),0(),(),(
),0(),0(
)1(
2
),0(
11)(
1
2
1)(
/'2'''(6)('
222
121
21
2
2
1
2
2
2
22
22
∫∫ b
a
xAcxb
a
xA dxexbaIdxexbaI )(332
)(331
2
),( ,),(
42
3)( bzz
czA
Free Energy
Phase Diagram
Speed of Sound
Parameter Dependence: Free Energy
42
3)( bzz
czA
Parameter Dependence:Phase Diagram
Lattice Calculations
μ = 0 heavy quarks
Fromm, Langelage, Lottini, Philipsen…
Summary• Einstein-Maxwell-dilaton system
• Potential reconstruction: analytic solution
• Linear Regge spectrum
• QCD phase diagram
• Mass dependent phase structure