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