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(1)

reference arXiv:1107.4048 (JHEP09 (2011) 073) with G. Mandal (Tata Institute in India)

from string theory?

Takeshi Morita KEK

22.2.2013 Seminar at NTU

(2)

``Quark-Gluon Plasma in QCD = Black Hole''

is predicted from AdS/CFT.

(3)

String theory tells us that this claim is suspicious.

``Quark-Gluon Plasma in QCD = Black Hole''

is predicted from AdS/CFT.

(4)

From Pisarski’s web site

Understanding of the finite temperature & finite density properties of QCD is the outstanding problem in theoretical physics.

RHIC quark star

early universe

◆ QCD

(5)

From Pisarski’s web site

Understanding of the finite temperature & finite density properties of QCD is the outstanding problem in theoretical physics.

QCD=YM+quark

Today we will mainly consider pure YM theory instead of QCD, since this theory is much simpler.

◆ QCD

(6)

From Pisarski’s web site

◆ SU(N) YM theory

confinement deconfinement

confinement/deconfinement transition

Entropy

YM theory also has an important phase structure.

(7)

◆ SU(N) YM theory

confinement deconfinement

confinement/deconfinement transition

Entropy

YM theory also has an important phase structure.

Since the system is strong coupling at low temperature, it is difficult to solve the phase structure.

Can we solve this issue by using holography?

(8)

◆ SU(N) YM theory

confinement deconfinement

confinement/deconfinement transition

Entropy

YM theory also has an important phase structure.

Since the system is strong coupling at low temperature, it is difficult to solve the phase structure.

Can we solve this issue by using holography?

A. It has not been solved yet, but there are many attempts. → Holographic QCD

(9)

◆ Holographic QCD

• D4 brane model (Witten's holographic QCD) Basic Idea:

D4 branes on a Scherk-Schwarz circle at weak coupling = 4dim pure YM theory D4 branes on a Scherk-Schwarz circle at strong coupling = IIA SUGRA

ADVANTAGES:

→ In principle, we can connect 4-dim YM at large N to SUGRA.

→ We can also obtain 4-dim QCD by adding D8 branes to this model.

(Sakai-Sugimoto model)

There are various holographic QCD models, but we will focus on the following model,

Currently only this model can connect 4-dim YM/QCD to string theory.

(10)

◆ Phase structures of the model - Black hole = QGP? -

Low temperature High temperature YM theory confinement deconfinement D4 brane model solitonic D4 black D4 brane

Entropy

It was believed that the black branes (≒ black hole) describe the deconfinement phase not only in this model but also in other holographic QCD models.

(11)

◆ Phase structures of the model - Black hole = QGP? -

Low temperature High temperature YM theory confinement deconfinement D4 brane model solitonic D4 black D4 brane

Entropy

NG

Today, I will show that this correspondence is not correct!

It was believed that the black branes (≒ black hole) describe the deconfinement phase not only in this model but also in other holographic QCD models.

(12)

◆ Phase structures of the model - Black hole = QGP? -

Low temperature High temperature YM theory confinement deconfinement D4 brane model solitonic D4 localized D3 soliton

Entropy

Today, I will show that this correspondence is not correct!

Instead I propose a new geometry, which is not a black object, will correspond to the deconfinement phase.

Since only the D4 brane model can connect the YM/QCD and string theory, we may have to reconsider the results derived by using black branes even in other holographic models, including the famous universal viscosity ratio

It was believed that the black branes (≒ black hole) describe the deconfinement phase not only in this model but also in other holographic QCD models.

(13)

◆ Phase structures of the model - Black hole = QGP? -

Low temperature High temperature YM theory confinement deconfinement D4 brane model solitonic D4 localized D3 soliton

Entropy

◆ Today's talk:

1. Overview of the D4 brane model.

2. Finite temperature in the D4 brane model.

3. Why the black brane is NG in the D4 brane model?

4. Modified phase structure in the D4 brane model.

5. Application to Sakai-Sugimoto model. (the chiral symmetry restoration) 6. Summary.

(14)

(0) 1 2 3 (4) 5 6 7 8 9 D4 - - - - -

0 and 4 directions are

◆Set up: IIA string theory in (Euclidean, finite temperature) Put N D4 branes as follows

◆ Effective theory of N D4 branes = 5-dim U(N) SYM.

5-dimensional gauge field

5 adjoint scalars → Represent the positions of D4 branes.

Fermions (super partner of the bosons)

N D4 (our 4-dimensional world)

(15)

(0) 1 2 3 (4) 5 6 7 8 9 D4 - - - - -

0 and 4 directions are

◆Set up: IIA string theory in (Euclidean, finite temperature) Put N D4 branes as follows

5-dimensional gauge field

5 adjoint scalars → Represent the positions of D4 branes.

Fermions (super partner of the bosons) : Impose anti-periodic (AP) boundary condition

on the fermions:

(Scherk-Schwarz circle)

→ mass → breaks supersymmetry

◆ Effective theory of N D4 branes = 5-dim U(N) SYM.

(16)

(0) 1 2 3 (4) 5 6 7 8 9 D4 - - - - -

0 and 4 directions are

◆Set up: IIA string theory in (Euclidean, finite temperature) Put N D4 branes as follows

: Impose anti-periodic (AP) boundary condition on the fermions:

(Scherk-Schwarz circle)

→ mass → breaks supersymmetry

5d SYM on

one-loop

: suppression of the loops from KK modes

: temperature ≪ KK scale

4d pure YM 4d limit

't Hooft coupling of 5dSYM and 4dYM

(17)

(0) 1 2 3 (4) 5 6 7 8 9 D4 - - - - -

0 and 4 directions are

◆Set up: IIA string theory in (Euclidean, finite temperature) Put N D4 branes as follows

: Impose anti-periodic (AP) boundary condition on the fermions:

(Scherk-Schwarz circle)

→ mass → breaks supersymmetry

5d SYM on

one-loop

: suppression of the loops from KK modes

: temperature ≪ KK scale

4d pure YM 4d limit

't Hooft coupling of 5dSYM and 4dYM Today's important parameters

(18)

◆ Phase structure of N D4 branes on

4dYM

AdS D4 soliton confinement phase

deconfinement phase confinement/deconfinement phase transition in 4dYM.

4dYM

?

?

?

?

?

?

5d SYM on

one-loop

: suppression of the loops from KK modes

: temperature ≪ KK scale

4d pure YM 4d limit

't Hooft coupling of 5dSYM and 4dYM

(19)

Solitonic D4

(Witten geometry/confinement geometry) The gravity description of the D4 branes works at large N and strong coupling . At low temperature , the solitonic D4 geometry appears as a stable solution.

This metric is obtained from a black brane by shifting f4(u) to the x4 coordinate.

(The details of the metric is not important in today's talk.)

N D4

◆ IIA SUGRA description at strong coupling

• Metric of solitonic D4 brane

(20)

◆ Phase structure of N D4 branes on

4dYM

AdS D4 soliton confinement phase

deconfinement phase confinement/deconfinement phase transition in 4dYM.

4dYM

?

?

?

?

?

?

SUGRA

Solitonic D4

This metric is obtained from a black brane by shifting f4(u) to the x4 coordinate.

(The details of the metric is not important in today's talk.)

• Metric of solitonic D4 brane

(21)

◆ Basic idea of the Witten's holographic QCD

4dYM

AdS D4 soliton confinement phase

deconfinement phase confinement/deconfinement phase transition in 4dYM.

4dYM

?

?

?

?

?

Solitonic D4 ?

We can extrapolate the 4d YM from IIA SUGRA through a strong coupling expansion.

SUGRA

SUGRA

(22)

Lattice gauge theory:

analytic result Lattice action (to use computer) 4d YM D4 brane model :

SUGRA result 5dSYM (to use D4 SUGRA) 4d YM

◆ Comparison to lattice gauge theory

continuum limit

◆ Basic idea of the Witten's holographic QCD

strong coupling expansion

SUGRA

Such a strong coupling expansion is usually not good at all quantitatively but is not so bad qualitatively as far as no phase transition occurs

between the strong coupling and weak coupling regions.

We also have to take care about unphysical mode like doubler in lattice.

(23)

Lattice gauge theory:

analytic result Lattice action (to use computer) 4d YM D4 brane model :

SUGRA result 5dSYM (to use D4 SUGRA) 4d YM continuum limit

◆ Basic idea of the Witten's holographic QCD

strong coupling expansion

Such a strong coupling expansion is usually not good at all quantitatively but is not so bad qualitatively as far as no phase transition occurs

between the strong coupling and weak coupling regions.

We also have to take care about unphysical mode like doubler in lattice.

• Actually several interesting results have been derived through this method.

• Sakai-Sugimoto added quarks to this model and also derived interesting results.

◆ Comparison to lattice gauge theory

(24)

SUGRA Experimental results

: input

◆ Ex) Baryon spectra in the Sakai-Sugimoto model

(Hata-Sakai-Sugimoto-Yamato 2007)

They roughly agree quantitatively!

Sakai-Sugimoto model

• Actually several interesting results have been derived through this method.

• Sakai-Sugimoto added quarks to this model and also derived interesting results.

◆ Basic idea of the Witten's holographic QCD

(25)

4dYM

AdS D4 soliton confinement phase

deconfinement phase confinement/deconfinement phase transition in 4dYM.

4dYM

?

?

?

?

?

Solitonic D4 ?

We can extrapolate the 4d YM from IIA SUGRA through the strong coupling expansion:

SUGRA

SUGRA

• Actually several interesting results have been derived through this method.

• Sakai-Sugimoto added quarks to this model and also derived interesting results.

◆ Basic idea of the Witten's holographic QCD

(26)

4dYM

AdS D4 soliton confinement phase

deconfinement phase confinement/deconfinement phase transition in 4dYM.

4dYM

?

?

?

We can extrapolate the 4d YM from IIA SUGRA through the strong coupling expansion:

SUGRA

???

It is quite natural idea to extend this analysis to finite temperature and study the properties of the confinement/deconfinement transition and QGP from the gravity.

Solitonic D4

◆ Basic idea of the Witten's holographic QCD

(27)

1. Overview of the D4 brane model.

2. Finite temperature in the D4 brane model.

3. Why the black brane is NG in the D4 brane model?

4. Modified phase structure in the D4 brane model.

5. Application to the Sakai-Sugimoto model.

6. Summary

(28)

(0) 1 2 3 (4) 5 6 7 8 9 D4 - - - - -

4d limit

◆ Two ways to obtain the finite temperature 4-dim YM theory

AP or P AP

AP b.c.:

P b.c.:

Regardless of the boundary condition, we obtain finite temperature 4d YM under the 4d limit, since the fermions become heavy and are decoupled.

→ Only F=0 dominates.

We have to fix the boundary condition of the fermions along the temporal circle.

(29)

(0) 1 2 3 (4) 5 6 7 8 9 D4 - - - - -

◆ Two ways to obtain the finite temperature 4-dim YM theory

AP or P AP

AP b.c.:

P b.c.:

Regardless of the boundary condition, we obtain finite temperature 4d YM under the 4d limit, since the fermions become heavy and are decoupled.

→ Only F=0 dominates.

However, the results of the SUGRA would depend on the boundary conditions, since the fermions are not decoupled.

→ We should study both b.c. in SUGRA.

(30)

(0) 1 2 3 (4) 5 6 7 8 9 D4 - - - - -

◆ Two ways to obtain the finite temperature 4-dim YM theory

AP or P AP

• Only the AP b.c. case has been studied and I will soon show that the black brane problem appears in this case. → next section

• The P b.c. can avoid this problem. → section 4.

• Potentially the AP b.c. can also avoid this problem. → Last section.

AP b.c.:

P b.c.:

4d limit

(31)

1. Overview of the D4 brane model.

2. Finite temperature in the D4 brane model.

3. Why the black brane is NG in the D4 brane model?

4. Modified phase structure in the D4 brane model.

5. Application to the Sakai-Sugimoto model.

6. Summary

(32)

(0) 1 2 3 (4) 5 6 7 8 9 D4 - - - - -

AP AP

We obtain a new solution by using this symmetry.

System has a symmetry:

◆ Gravity solutions in the AP b.c. case

Black D4 solution:

This solution is stable at high temperature

Solitonic D4 (confinement geometry) Entropy

(33)

Black D4

IIA SUGRA

guess

Solitonic D4

◆ Phase structure of N D4 branes on (AP b.c.)

Black D4 solution:

This solution is stable at high temperature

Solitonic D4 (confinement geometry) Entropy

4dYM SUGRA

confinement phase deconfinement phase

4dYM

Aharony-Sonnenschein-Yankielowicz 2006 Mandal-T.M. 2011

(34)

Black D4

IIA SUGRA

guess

Solitonic D4

◆ Phase structure of N D4 branes on (AP b.c.)

4dYM SUGRA

confinement phase deconfinement phase

4dYM

Aharony-Sonnenschein-Yankielowicz 2006 Mandal-T.M. 2011

The famous review paper of AdS/CFT by Aharony, Gubser, Maldacena, Ooguri and Oz (citation is more than 2800!) claimed that the phase transition between the Solitonic D4 and black D4 corresponds to the confinement/deconfinement transition in the 4d YM.

→ Many people have believed it.

(35)

Black D4

IIA SUGRA

guess

Solitonic D4

◆ Phase structure of N D4 branes on (AP b.c.)

4dYM SUGRA

confinement phase deconfinement phase

4dYM

Aharony-Sonnenschein-Yankielowicz 2006 Mandal-T.M. 2011

→ However, this claim is wrong!

The famous review paper of AdS/CFT by Aharony, Gubser, Maldacena, Ooguri and Oz (citation is more than 2800!) claimed that the phase transition between the Solitonic D4 and black D4 corresponds to the confinement/deconfinement transition in the 4d YM.

→ Many people have believed it.

(36)

Black D4

IIA SUGRA

guess

A B

guess

C

Solitonic D4

• At least 3 phases (A,B,C) exist in this system!

• These phases are distinguished by VEVs of the Wilson loops winding and .

• Black D4 and the deconfinement phase in 4dYM belong to different phases (C and B).

→ The strong coupling expansion would not work owing to the phase transition.

• KK reduction to 4d YM does not work in phase C due to the large N volume independence.

→ Black D4 brane is nothing to do with the 4d YM.

4dYM SUGRA

confinement phase deconfinement phase

4dYM

Aharony-Sonnenschein-Yankielowicz 2006 Mandal-T.M. 2011

◆ Phase structure of N D4 branes on (AP b.c.)

(37)

deconfinement C/D transition

Black D4 brane

The symmetry ensures the existence of the three phases at least.

Solitonic D4

Another phase transition which is the mirror of the C/D transition.

A

B

C

Aharony-Sonnenschein-Yankielowicz 2006 Mandal-T.M. 2011

◆ Phase structure at fixed

◆ Phase structure of N D4 branes on (AP b.c.)

(38)

◆ Phase structure of N D4 branes on (AP b.c.)

Black D4

IIA SUGRA

guess

A B

guess

C

Solitonic D4

• At least 3 phases (A,B,C) exist in this system!

• These phases are distinguished by VEVs of the Wilson loops winding and .

• Black D4 and the deconfinement phase in 4dYM belong to different phases (C and B).

→ The strong coupling expansion would not work owing to the phase transition.

• KK reduction to 4d YM does not work in phase C due to the large N volume independence.

→ Black D4 brane is nothing to do with the 4d YM.

4dYM SUGRA

confinement phase deconfinement phase

4dYM

Aharony-Sonnenschein-Yankielowicz 2006 Mandal-T.M. 2011

(39)

◆ KK reduction and phases

• KK reduction to 4d YM does not work in phase C due to the large N volume independence.

→ Black D4 brane is nothing to do with the 4d YM.

5d SYM on

one-loop

: suppression of the loops from KK modes

: temperature ≪ KK scale

4d pure YM 4d limit

't Hooft coupling of 5dSYM and 4dYM

This estimate of the KK mass scale is through a perturbative calculation, and it can fail depending on the phases.

→ We can show that the KK mass scale at the phase C is rather than and the KK reduction does not work at large N.

(Large N volume independence )

Eguchi-Kawai 1982, Gocksch-Neri 1983, Kovtun-Unsal-Yaffe 2007 Mandal-T.M. 2011

(40)

◆ Phase structure of N D4 branes on (AP b.c.)

Black D4

IIA SUGRA

guess

A B

guess

C

Solitonic D4

• At least 3 phases (A,B,C) exist in this system!

• These phases are distinguished by VEVs of the Wilson loops winding and .

• Black D4 and the deconfinement phase in 4dYM belong to different phases (C and B).

→ The strong coupling expansion would not work owing to the phase transition.

• KK reduction to 4d YM does not work in phase C due to the large N volume independence.

→ Black D4 brane is nothing to do with the 4d YM.

4dYM SUGRA

confinement phase deconfinement phase

4dYM

Aharony-Sonnenschein-Yankielowicz 2006 Mandal-T.M. 2011

(41)

1. Overview of the D4 brane model.

2. Finite temperature in the D4 brane model.

3. Why the black brane is NG in the D4 brane model?

4. Modified phase structure in the D4 brane model.

5. Application to the Sakai-Sugimoto model.

6. Summary

(42)

(0) 1 2 3 (4) 5 6 7 8 9 D4 - - - - -

P AP

◆ Two ways to obtain the finite temperature 4-dim YM theory

Now we consider SUGRA in the P b.c. case.

(43)

◆ Phase structure of N D4 branes on (P b.c.)

IIA SUGRA

GL transition

confinement phase

deconfinement phase confinement/deconfinement phase transition in 4dYM.

localized D3 soliton

IIB SUGRA

?

A B

• Only two phases (A and B) appear and the KK reduction is possible in both phases.

•The high temperature solution in SUGRA and the deconfinement phase in the 4d YM belong to the same phase (phase B).

• However we have to take a T-dual on to see the phase transition at high temperature in SUGRA.

Solitonic D4

T-dual on

smeared D3 soliton

4dYM

SUGRA

4dYM

(44)

Solitonic D4 (IIA SUGRA)

The winding string along becomes light.

→ IIA SUGRA description is not valid above this temp..

N D4 brane

◆ High temperature properties of IIA/IIB SUGRA

: IIB SUGRA description becomes valid from this temp..

◆ T-dual on

D4 wrapping D3 localized on IIA string IIB string

momentum

winding mode momentum

winding mode

D3 brane

: positions of D3 branes on

(45)

Solitonic D4 (IIA SUGRA)

The winding string along becomes light.

→ IIA SUGRA description is not valid above this temp..

N D4 brane

◆ High temperature properties of IIA/IIB SUGRA

: IIB SUGRA description becomes valid from this temp..

D3 brane

Smeared D3 soliton (IIB SUGRA)

N D3 branes uniformly distributed along

Note: This is not a phase transition.

(46)

◆ Phase structure of N D4 branes on (P b.c.)

IIA SUGRA

GL transition

confinement phase

deconfinement phase confinement/deconfinement phase transition in 4dYM.

localized D3 soliton

IIB SUGRA

?

A B

• Only two phases (A and B) appear and the KK reduction is possible in both phases.

•The high temperature solution in SUGRA and the deconfinement phase in the 4d YM belong to the same phase (phase B).

• However we have to take a T-dual on to see the phase transition at high temperature in SUGRA.

Solitonic D4

T-dual on

smeared D3 soliton

4dYM

SUGRA

4dYM

(47)

Solitonic D4 (IIA SUGRA)

The winding string along becomes light.

→ IIA SUGRA description is not valid above this temp..

N D4 brane

◆ High temperature properties of IIA/IIB SUGRA

: IIB SUGRA description becomes valid from this temp..

D3 brane

Smeared D3 soliton (IIB SUGRA)

N D3 branes uniformly distributed along

(48)

Solitonic D4 (IIA SUGRA)

The winding string along becomes light.

→ IIA SUGRA description is not valid above this temp..

N D4 brane

◆ High temperature properties of IIA/IIB SUGRA

: IIB SUGRA description becomes valid from this temp..

D3 brane

Smeared D3 soliton (IIB SUGRA)

N D3 branes uniformly distributed along

Localized D3 soliton (IIB SUGRA)

N D3 branes localized on

Gregory-Laflamme type transition

(49)

D3 brane

→ If the radius of is large (high temperature), the black string is unstable due to the GL instability.

→ The horizon tends to shrink, and a black hole

localized on becomes stable at high temperature.

◆ Gregory-Laflamme (GL) type transition at high temperature.

AP P

If we regard x4 as a``time" direction and t' as a ``spatial'' direction, this metric is just a black string whose horizon is winding .

Metric of the Smeared D3 soliton (IIB SUGRA)

black string (smeared D3 soliton)

localized black hole (localized D3 soliton)

(50)

◆ Phase structure of N D4 branes on (P b.c.)

IIA SUGRA

GL transition

confinement phase

deconfinement phase confinement/deconfinement phase transition in 4dYM.

localized D3 soliton

IIB SUGRA

?

A B

Solitonic D4

T-dual on

smeared D3 soliton

4dYM

SUGRA

4dYM

• The GL transition in IIB SUGRA would be related to

the confinement/deconfinement transition in the 4 dim YM theory.

• The deconfinement phase is related to the localized D3 soliton.

(51)

◆ Why is the GL transition related to the C/D transition?

→ Both transitions may be related to the Hagedron instability .

(52)

GL instability

Momentum instability along

IIB IIA

◆ Why is the GL transition related to the C/D transition?

→ Both transitions may be related to the Hagedron instability .

Momentum in IIB

= Winding in IIA

→ unstable string winding

along

(53)

GL instability

Momentum instability along

IIB IIA

cf. Atick-Witten

C/D transition in 4d YM

→ Hagedron instability

→ Unstable QCD string winding

4d limit

(weak coupling)

◆ Why is the GL transition related to the C/D transition?

→ Both transitions may be related to the Hagedron instability .

Momentum in IIB

= Winding in IIA

→ unstable string winding

along

(54)

◆ Phase structure of N D4 branes on (P b.c.)

IIA SUGRA

GL transition

confinement phase

deconfinement phase confinement/deconfinement phase transition in 4dYM.

localized D3 soliton

IIB SUGRA

?

A B

Solitonic D4

T-dual on

smeared D3 soliton

4dYM

SUGRA

4dYM

• The GL transition in IIB SUGRA would be related to the C/D transition.

• A SUSY lattice calculation of N D1 brane (2d SYM) also reproduce the similar phase structure.

If D4 and D1 are similar, the above speculation would be correct.

(Catterall-Joseph-Wiseman 2010)

(55)

1. Overview of the D4 brane model.

2. Finite temperature in the D4 brane model.

3. Why the black brane is NG in the D4 brane model?

4. Modified phase structure in the D4 brane model.

5. Application to the Sakai-Sugimoto model.

6. Summary

(56)

◆ Chiral symmetry restoration in QCD

Chiral symmetry is preserved.

Chiral symmetry is broken.

Can holographic QCD explain the chiral symmetry breaking/restoration?

This is very important since it opens up a possibility of the understanding of the QCD phase diagram, e.g. chemical potential and magnetic field dependence of chiral transition.

(57)

chiral symmetry is realized as the gauge sym on branes.

Put branes on the D4 brane geometry and ignore their backreaction (probe approximation )

Sakai-Sugimoto 2004

relevant massless fields: gluon+quarks = realistic QCD model

Same to the D4 brane model

SU(N) gluon

massless quarks

Sakai and Sugimoto showed that this chiral symmetry is broken at low temperature.

We can expect that the chiral symmetry would be restored at a higher temperature as in the real QCD.

c.f. Aharony, Sonnenschein, Yankielowicz (2006) showed it by using

the black D4 brane geometry, which is not related to the deconfinement phase anymore…

◆ Sakai-Sugimoto model

(58)

◆ Chiral symmetry breaking in a low temperature phase

Sakai-Sugimoto 2004

are separated. are connected.

D4 soliton (confinement geometry)

(59)

◆ Chiral symmetry restoration at a high temperature

A subtle issue: We will use the P boundary condition along the t-cirlce, and the periodicity of the quarks is different from the standard anti-periodicity.

We can avoid this issue by using imaginary baryon chemical potential.

(Today I will skip this point.)

Sakai-Sugimoto model

T-dual along the t-circle

Evaluate the possible D7 brane configurations after taking the T-duality.

Strategy

(60)

T-dual along the t-circle

◆ Chiral symmetry restoration at a high temperature

(61)

the GL transition in the IIB

◆ Chiral symmetry restoration at a high temperature

(62)

All transitions are 1st order.

◆ Chiral symmetry restoration at a high temperature

(63)
(64)

We are ready to study the full phase diagram of the large-N QCD.

• String theory indicates QGP ≠ black hole in holographic QCD.

• We find an alternative solution ``localized soliton" related to deconf. phase.

• We also find a correct mechanism of the chiral symmetry restoration

at the deconfinement phase in the Sakai-Sugimoto model.

(65)

• String theory indicates QGP ≠ black hole in holographic QCD.

• We find an alternative solution ``localized soliton" related to deconf. phase.

• We also find a correct mechanism of the chiral symmetry restoration at the deconfinement phase in the Sakai-Sugimoto model.

Future works

• Real time dynamics:

It is unclear how to evaluate real time physics from the localized soliton in GR.

Due to this issue, we cannot calculate the viscosity in this geometry.

• 4d YM from AP b.c.: If we drop the black D4 brane by hand as an unphysical phase, we might obtain a similar phase structure to the P b.c. case.

Then the whole picture becomes consistent.

AP b.c.:

P b.c.:

(66)

Future works

• Real time dynamics:

It is unclear how to evaluate real time physics from the localized soliton in GR.

Due to this issue, we cannot calculate the viscosity in this geometry.

• 4d YM from AP b.c.: If we drop the black D4 brane by hand as an unphysical phase, we might obtain a similar phase structure to the P b.c. case.

Then the whole picture becomes consistent.

AP b.c.:

P b.c.:

Black D4

guess

A B

guess

C

Solitonic D4

guess

A B

Solitonic D4

??

(67)
(68)

◆ Black hole solutions on in IIB SUGRA

black string (smeared soliton)

→ confinement

localized black hole (localized soliton)

→ deconfinement

multi localized black hole (multi localized soliton)

In addition to these two solutions, infinite number of unstable multi-black hole solutions are known in gravity.

→ corresponding unstable phases may exist in the YM theory

Harmark-Obers 2004, Azuma-T.M.-Takeuchi 2012

→ We find these new unstable phases in YM through

a perturbative calculation at high temperature.

(69)

◆ Black hole solutions on in IIB SUGRA

black string (smeared soliton)

→ confinement

localized black hole (localized soliton)

→ deconfinement

multi localized black hole

(multi localized soliton)

ex) 2 localized BHs

(70)

◆ Black hole solutions on in IIB SUGRA

black string (smeared soliton)

→ confinement

localized black hole (localized soliton)

→ deconfinement

multi localized black hole (multi localized soliton)

In addition to these two solutions, infinite number of unstable multi-black hole solutions are known in gravity.

→ corresponding unstable phases may exist in the YM theory

Harmark-Obers 2004, Azuma-T.M.-Takeuchi 2012

→ We find these new unstable phases in YM through

a perturbative calculation at high temperature.

(71)

◆ New unstable branches of 4d YM theory at finite temperature

confinement deconfinement

2 BHs 3 BHs

C/D transition

→ We find these new unstable phases in YM through a perturbative calculation at high temperature.

large N pure YM

(72)

◆ New unstable branches of 4d YM theory at finite temperature

2 BHs 3 BHs

C/D transition

◆ Order parameter: Generalized Polyakov loop

confinement phase : deconfinement phase (1 BH):

3 BH:

→ We find these new unstable phases in YM through a perturbative calculation at high temperature.

large N pure YM

(73)

◆ New unstable branches of 4d YM theory at finite temperature

2 BHs 3 BHs

C/D transition

◆ Order parameter: Generalized Polyakov loop

confinement phase : deconfinement phase (1 BH):

3 BH:

•These phases generally exist in wide class of SU(N) and U(N) gauge theories including QCD and SYM even at finite N, if N≧3.

•We can show that these new states play important role in certain real-time dynamics.

(See our paper)

large N pure YM

參考文獻

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