is ``quark-gluon plasma = black hole'' in string theory?€¦ · black brane (≒ black...

reference arXiv:1107.4048 (JHEP09 (2011) 073)

with G. Mandal (Tata Institute in India)

Is ``Quark-Gluon Plasma = Black Hole''

in string theory?

Takeshi Morita

PD, KEK (→ PD, Kentucky university (from October, 2013))

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

is predicted from AdS/CFT.

You may have heard the claim:

You may have heard the claim:

String theory tells us that this claim is suspicious.

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

is predicted from AdS/CFT.

From Pisarski’s web site

QCD at finite temperature → important in our real world

RHIC quark star

early universe

◆ QCD

Introduction


QCD=YM+quark

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

◆ QCD

Introduction

QCD at finite temperature → important in our real world


◆ SU(N) YM theory

confinement

deconfinement

confinement/deconfinement transition

Entropy YM theory also has an important phase structure.

Introduction

◆ SU(N) YM theory

confinement

deconfinement



Introduction

Can we solve YM by holography?

◆ SU(N) YM theory

confinement

deconfinement



Can we solve YM by holography?

Introduction

A. It has NOT been solved,

but there are many attempts.

→ Holographic QCD

◆ Holographic QCD

◆ D4 brane model (Witten's holographic QCD)

ADVANTAGES: → In principle, we can connect 4-dim pure 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.

Introduction

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

Low temperature High temperature

YM theory confinement deconfinement

D4 brane model solitonic D4 black D4 brane (≒ black hole)

Entropy

Introduction


D4 brane model solitonic D4 black D4 brane (≒ black hole)



Entropy

Introduction

NG

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




D4 brane model solitonic D4 localized D3 soliton

Entropy

Introduction

Other solution (NOT a black object) corresponds to the deconfinement phase.





Entropy

Introduction

In the Sakai-Sugimoto model, many papers studied this region by using the black D4 brane.

→ We need to reconsider them.





Entropy

Introduction

Black brane (≒ black hole) = deconfinement phase

is believed not only in this model but also in other holographic QCD models.

(c.f. This relation will be true in the SYM theories.)

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





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. Summary.

Introduction

1. Overview of the D4 brane model

(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)

Witten 1998

N D4 (our 4-dimensional world)


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

D4 - - - - -




5-dimensional gauge field

5 adjoint scalars → Represent the positions of D4 branes.

Fermions (super partner of the bosons)

Witten 1998

: 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.


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

D4 - - - - -




Witten 1998


on the fermions:



5d SYM on

one-loop

't Hooft coupling of 5dSYM


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

D4 - - - - -




Witten 1998


on the fermions:



5d SYM on

one-loop

: << KK scale ( : dynamical scale of YM)

: temperature ≪ KK scale

4d pure YM

4d limit



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

D4 - - - - -




Witten 1998


on the fermions:



5d SYM on

one-loop 4d pure YM

4d limit

Today's important parameters

: << KK scale ( : dynamical scale of YM)



◆ Phase structure of N D4 branes on

1. Overview of the D4 brane model Witten 1998

4dYM

AdS D4 soliton

confinement phase

deconfinement phase confinement/deconfinement phase transition in 4dYM.

4dYM

?

?

? ?

?

?

5d SYM on

one-loop 4d pure YM

4d limit : << KK scale ( : dynamical scale of YM)




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

◆ Phase structure of N D4 branes on


4dYM

AdS D4 soliton

confinement phase


4dYM

?

?

? ?

?

? 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

◆ Basic idea of the Witten's holographic QCD


4dYM

AdS D4 soliton

confinement phase


4dYM

?

?

? ?

?

? Solitonic D4

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

SUGRA ( << KK scale)


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


strong coupling expansion

SUGRA

Such a strong coupling expansion is not so bad qualitatively, IF

1. No phase transition occurs between the strong and weak coupling regions.

2. Take care about unphysical mode like doubler in lattice.

( << KK scale)

( << KK scale)

( << 1/a, a: lattice space)

continuum limit ("weak" coupling)



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

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

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 ("weak" coupling)

strong coupling expansion

Such a strong coupling expansion is not so bad qualitatively, IF

1. No phase transition occurs between the strong and weak coupling regions.

2. Take care about unphysical mode like doubler in lattice.

( << KK scale)

( << 1/a, a: lattice space)

◆ Comparison to lattice gauge theory


SUGRA

Experimental data

: input

◆ Ex) Baryon spectra in the Sakai-Sugimoto model (Hata-Sakai-Sugimoto-Yamato 2007)

They roughly agree quantitatively!

Sakai-Sugimoto model (After removing unphysical modes.)





4dYM

AdS D4 soliton

confinement phase


4dYM

?

?

? ?

?

? Solitonic D4

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

SUGRA





4dYM

AdS D4 soliton

confinement phase


4dYM ?

?

?

???

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


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




4. Modified phase structure in the D4 brane model.

5. Summary

(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 AP or P

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.

2. Finite temperature in the D4 brane model Mandal-T.M. 2011

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

D4 - - - - -

4d limit


AP AP or P

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.

2. Finite temperature in the D4 brane model Mandal-T.M. 2011

We should test both b.c. in SUGRA.



3. SUGRA with the AP b.c. Why the black brane is NG in the D4 brane model?

4. SUGRA with the P b.c. Modified phase structure in the D4 brane model.

5. Summary

(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

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

Black D4

IIA SUGRA

guess Solitonic D4



4dYM

SUGRA

confinement phase

deconfinement phase

4dYM

Black D4 brane deconfinement phase in 4dYM ?

Aharony, Gubser, Maldacena, Ooguri and Oz (1999)

Black D4

IIA SUGRA

guess Solitonic D4



4dYM

SUGRA

confinement phase

deconfinement phase

4dYM

Black D4 brane deconfinement phase in 4dYM ?

Aharony, Gubser, Maldacena, Ooguri and Oz (1999)

This claim is not correct.

Black D4

IIA SUGRA

guess

A

B

C guess

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.

4dYM

SUGRA

confinement phase

deconfinement phase

4dYM

Aharony-Sonnenschein-Yankielowicz 2006

Mandal-T.M. 2011


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


Mandal-T.M. 2011 ◆ Phase structure at fixed


4dYM confinement

4dYM

SUGRA


Black D4

IIA SUGRA

guess

A

B

C guess

Solitonic D4





4dYM

SUGRA

confinement phase

deconfinement phase

4dYM


Mandal-T.M. 2011


Black D4

IIA SUGRA

guess

A

B

C guess

Solitonic D4





• 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


Mandal-T.M. 2011


Black D4

IIA SUGRA

guess

A

B

C guess

Solitonic D4


4dYM

SUGRA

confinement phase

deconfinement phase

4dYM


Mandal-T.M. 2011

Black D4 brane ≠ deconfinement phase in 4dYM → An ``artifact'' of the D4 brane model (AP b.c.)



Black D4

guess

A

B C

guess

Solitonic D4 guess

A

B Solitonic D4

??

To see 4dYM, we should remove Black D4 by hand. → However, the gravity analysis at high temperature is difficult in the AP b.c. case...

→ We can avoid this difficulty in the P b.c. case!

Black D4 brane ≠ deconfinement phase in 4dYM → An ``artifact'' of the D4 brane model (AP b.c.)



3. SUGRA with the AP b.c. Why the black brane is NG in the D4 brane model?

4. SUGRA with the P b.c. Modified phase structure in the D4 brane model.

5. Summary

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

D4 - - - - -

AP P

Mandal-T.M. 2011


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

4. Modified phase structure in the D4 brane model

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

IIA SUGRA

GL transition

confinement phase


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

Mandal-T.M. 2011

4dYM

SUGRA

4dYM


Solitonic D4 (IIA SUGRA)

The winding string along becomes light. → IIA SUGRA description is not valid above this temp..

N D4 brane

Mandal-T.M. 2011

◆ High temperature properties of IIA/IIB SUGRA

: IIB SUGRA description becomes valid from this temp..

◆ T-dual on (P b.c.)

IIA string IIB string

D3 brane


cf. T-dual on (AP b.c.)

IIA string 0B string


IIA SUGRA

GL transition

confinement phase



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

Mandal-T.M. 2011

4dYM

SUGRA

4dYM



IIA SUGRA

GL transition

confinement phase



IIB SUGRA

?

A

B

Solitonic D4

T-dual on

smeared D3 soliton

Mandal-T.M. 2011

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.



IIA SUGRA

GL transition

confinement phase



IIB SUGRA

?

A

B

Solitonic D4

T-dual on

smeared D3 soliton

Mandal-T.M. 2011 4. Modified phase structure in the D4 brane model

4dYM

SUGRA

4dYM

• A SUSY lattice calculation of N D1 brane (2d SYM) also shows a similar phase structure. If D4 and D1 are similar, the above speculation would be correct.

(Catterall-Joseph-Wiseman 2010)

Summary

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

Summary

• 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 (skipped today).

Summary

Future works

AP b.c.:

P b.c.:

• 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 (skipped today).

• 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 remove the black D4 brane by hand, we might obtain a similar phase structure to the P b.c. case. → 0B string Then the whole picture becomes consistent.

Future works

AP b.c.:

P b.c.:

Black D4

guess

A

B C

guess

Solitonic D4 guess

A

B Solitonic D4

??

Phase structure in AP b.c. Phase structure in AP b.c.

• 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 remove the black D4 brane by hand, we might obtain a similar phase structure to the P b.c. case. → 0B string Then the whole picture becomes consistent.

Thanks

is ``quark-gluon plasma = black hole'' in string theory?€¦ · black brane (≒ black...

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