AdS/CFT-QCD-CMT

Yi Yang@NCTU&NCTS

NTHU April 8th, 2010

Contents

• D-brane (1995)

• AdS/CFT (1997)

• AdS/QCD (2004)

• AdS/CMT (2008)

+ + …

Perturbative Strings

Non-Perturbative Objects•Solitions

•RR sources

•Ends of open strings

D-branes (1995)

Branes Scenario

D3 branes and • N charged D3-brane

•Extreme limit

•Near horizon

0 rr

0r

25

222

222

2

22 dRdr

r

Rdxdt

R

rds i

55 SAdS

Open/Closed strings duality•Open strings

•Closed strings

spacehorizon near on StringsSG Free SSS

braneSG Free SSS

AdS/CFT in Type IIB•AdS/CFT conjecture (1997)

•N=4 SYM in 3+1 IIB on

•The precise relationship (1998) xzxZe

xxxd

0StringCFT

0,04

55 SAdS

Holography

Strong/Weak duality

•Effective coupling:

•Small curvature for SG:

•Small coupling in SG:

RNgs

11 Ngs

1R

Gravity/Gauge duality

String theory Gauge theory

IIB Strings on N=4 SYM

Strings on deformed AdS strong coupling theory?

55 SAdS

AdS/QCD(Sakai-Sugimoto Model)

0 1 2 3 4 5 6 7 8 0

D4 ● ● ● ● ●

D8-D8 ● ● ● ● ● ● ● ● ●

String Picture

Gravity Picture: Low T

Phase Transition

cTT cTT ~ cTT

Gravity Picture: High T

QCD Phase Diagram

Baryons as Wrapped D-brane

AdS/CMT(Superconductor)

•Einstein-Maxwell-charged scalar

•Backreaction and probe•Instability and symmetry breaking

22222

4

4

16 miqAFL

RxdS

Schwarzschild AdS Black Hole

)()(

)( 2222

22 dydxrrf

drdtrfds

3

3

2

2

1)(r

r

L

rrf

Probe Fields•Probe ansatz

•At horizon•At boundary

0 ,)( ,)( yxrtt AAArAAr

0tA

rr

O

r

O 221 ，

Condensation

Hairy Black Hole

3 hairs scalar hair

Conductivity•Fluctuations of gauge field

•At boundary

•AdS/CFT dictionary

•Ohm’s law

tixx erArtA )(),(

r

AArA x

xx

)1()0()(

)1()0( , xxxx AJAA

)0(

)1(

)(x

x

x

x

x

x

x

x

A

iA

A

Ji

A

J

E

J

Gap

Magnetic Field•Meissner effect

•Type I superconductor

•Type II superconductor

)()(8

)(TFTF

VTBsn

c

u

uur

at constant

0at 0 ),(

Other models

•Charged dilaton black hole

•Chern-Simon’s term

•Probe D-branes

•String background

Summary

AdS/CFT (1997)

AdS/QCD (2004)

AdS/CMT (2008)

AdS/??? (20XX)