based on arXiv:1107.xxxx with G. Mandal (TIFR)

What is the gravity dual of

the confinement/deconfinement transportation

in holographic QCDTakeshi Morita

University of Crete

1. Introduction

◆ Holographic construction of “4d pure Yang-Mills”Witten 1998, AGMOO 1999

confinement/deconfinement transition

4 dim SU(N) YM ← 5dim SU(N) SYM = N D4 brane Scherk-Schwarz mechanism

D4 soliton/black D4 transition

Aharony, Sonnenschein, Yankielowicz 2006

Aharony, Minwalla, Wiseman

Mandal, T.M. 2011

Several problems have been reported

in this identification.

1. Introduction

◆ Holographic construction of “4d pure Yang-Mills”Witten 1998, AGMOO 1999

confinement/deconfinement transition

4 dim SU(N) YM ← 5dim SU(N) SYM = N D4 brane Scherk-Schwarz mechanism

D4 soliton/black D4 transitionD4 soliton/D3 soliton transition

Aharony, Sonnenschein, Yankielowicz 2006

Aharony, Minwalla, Wiseman

Mandal, T.M. 2011

Several problems have been reported

in this identification.

◆ Holographic construction of “4d pure Yang-Mills”Witten 1998, AGMOO 1999

confinement/deconfinement transition

4 dim SU(N) YM ← 5dim SU(N) SYM = N D4 brane Scherk-Schwarz mechanism

D4 soliton/black D4 transition

1. Introduction

2. Review of holographic QCD

3. Problem of the previous interpretation of the C/D transition

4. Our proposal

5. Conclusion

Plan of my talk

Sec.2

Sec.3Sec.4

D4 soliton/D3 soliton transition

2. Review of holographic QCD

(Witten 1998)

: anti-periodic (AP) boundary condition

for fermions

(Scherk-Schwarz circle)

→ mass → breaks supersymmetry

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

0 and 4 are periodic coordinates.

one-loop

5d SYM on 4d pure YM

: suppression of the loops

from KK modes

: temperature ≪ KK scale

4d limit

2. Review of holographic QCD

◆ Holographic 4d pure YM

IIA SUGRA

5d SYM on

4d pure YM

Important pointGravity can describe the 5d SYM but not the 4d YM.

We always need to extrapolate the information of the 4dYM from the 5d SYM!

(Witten 1998)

2. Review of holographic QCD

IIA SUGRA

5d SYM on

4d pure YM

Important pointGravity can describe the 5d SYM but not the 4d YM.

We always need to extrapolate the information of the 4dYM from the 5d SYM!

By using some prescriptions, we can obtain “4d YM” results from the gravity.

These results agree with 4d YM/QCD qualitatively and sometimes quantitatively. (Sakai-Sugimoto)

•ignore fermions

•ignore SO(4) non-singlet

•etc…

(Witten 1998)

◆ Holographic 4d pure YM

2. Review of holographic QCD

IIA SUGRA

5d SYM on

4d pure YM

•ignore fermions

•ignore SO(4) non-singlet

•etc…

A corresponding phase transition may appear in IIA SUGRA.

the confinement/deconfinement transition??

Finite temperature

(Witten 1998)

◆ Holographic 4d pure YM

◆ Holographic construction of “4d pure Yang-Mills”Witten 1998, AGMOO 1999

confinement/deconfinement transition

4 dim SU(N) YM ← 5dim SU(N) SYM = N D4 brane Scherk-Schwarz mechanism

D4 soliton/black D4 transition

1. Introduction

2. Review of holographic QCD

3. Problem of the previous interpretation of the C/D transition

4. Our proposal

5. Conclusion

Plan of my talk

Sec.2

Sec.3Sec.4

D4 soliton/D3 soliton transition

In finite temperature case, we need to fix the boundary condition of the fermion along

◆ AdS soliton/black brane as the confinement/deconfinement transition?

: AP boundary condition for fermions

(Scherk-Schwarz circle)

→ mass → breaks supersymmetry

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

3. confinement/deconfinement transition in holographic QCD

In previous studies, people used the AP boundary condition along

as in the standard thermodynamics.

The system has a

3. confinement/deconfinement transition in holographic QCD

AdS D4 soliton (confinement geometry)

Black D4 solution

Since the black D4 is obtained by , a first order phase transition happens at

This phase transition is sometimes called Scherk-Schwarz (SS) transition.

(We can see this transition by comparing the free energies.)

Black D4 solution AdS D4 solitonSS transition

◆ AdS soliton/black brane as the confinement/deconfinement transition?

3. confinement/deconfinement transition in holographic QCD

AdS D4 soliton vs Black D4 solution

confinement phase vs deconfinement phase

a confinement/deconfinement transition

IIA SUGRA

4d pure YMSS transition at

We can observe the similarities between them.

3. confinement/deconfinement transition in holographic QCD

AdS D4 soliton Black D4 solution

4d pure YM

confinement phase

confinement/deconfinement transition

deconfinement phase

IIA SUGRA Scherk-Schwarz transition

These correspondences were supposed to be natural.

However, a serious problem was found….

Aharony, Sonnenschein, Yankielowicz 2006

Aharony, Minwalla, Wiseman

◆ AdS soliton/black brane as the confinement/deconfinement transition?

◆ Phase structure of the 5dSYM

3. confinement/deconfinement transition in holographic QCD

4dYM

AdS D4 soliton

Black D4

IIA SUGRA

SS transition

Since the Scherk-Schwarz transition at is a consequence of ,

even if we consider stringy effects, it must not continue to

the confinement/deconfinement transition in the 4dYM.

confinement phase

confinement/deconfinement phase transition in 4dYM.

A transition obtained from

The black D4 solution must not correspond to the deconfinement phase in 4dYM.

Aharony, Sonnenschein, Yankielowicz 2006

Aharony, Minwalla, Wiseman

deconfinement phase

4dYM

GR

◆ Phase structure of the 5dSYM

3. confinement/deconfinement transition in holographic QCD

4dYM

AdS D4 soliton

Black D4

IIA SUGRA

SS transition

Since the Scherk-Schwarz transition at is a consequence of ,

even if we consider stringy effects, it must not continue to

the confinement/deconfinement transition in the 4dYM.

confinement phase

confinement/deconfinement phase transition in 4dYM.

A transition obtained from

The black D4 solution must not correspond to the deconfinement phase in 4dYM.

Aharony, Sonnenschein, Yankielowicz 2006

Aharony, Minwalla, Wiseman

deconfinement phase

4dYM

GR

◆ Phase structure of the 5dSYM

3. confinement/deconfinement transition in holographic QCD

4dYM

AdS D4 soliton

Black D4

IIA SUGRA

SS transition

Since the Scherk-Schwarz transition at is a consequence of ,

even if we consider stringy effects, it must not continue to

the confinement/deconfinement transition in the 4dYM.

confinement phase

confinement/deconfinement phase transition in 4dYM.

A transition obtained from

The black D4 solution must not correspond to the deconfinement phase in 4dYM.

Aharony, Sonnenschein, Yankielowicz 2006

Aharony, Minwalla, Wiseman

deconfinement phase

4dYM

GR

◆ Phase structure of the 5dSYM

3. confinement/deconfinement transition in holographic QCD

4dYM

AdS D4 soliton

Black D4

IIA SUGRA

SS transition

Since the Scherk-Schwarz transition at is a consequence of ,

even if we consider stringy effects, it must not continue to

the confinement/deconfinement transition in the 4dYM.

confinement phase

confinement/deconfinement phase transition in 4dYM.

A transition obtained from

guess

The black D4 solution must not correspond to the deconfinement phase in 4dYM.

Aharony, Sonnenschein, Yankielowicz 2006

Aharony, Minwalla, Wiseman

deconfinement phase

4dYM

GR

◆ Phase structure of the 5dSYM

3. confinement/deconfinement transition in holographic QCD

4dYM

AdS D4 soliton

Black D4

IIA SUGRA

SS transition

Since the Scherk-Schwarz transition at is a consequence of ,

even if we consider stringy effects, it must not continue to

the confinement/deconfinement transition in the 4dYM.

confinement phase

confinement/deconfinement phase transition in 4dYM.

A transition obtained from

guess

The black D4 solution must not correspond to the deconfinement phase in 4dYM.

Aharony, Sonnenschein, Yankielowicz 2006

Aharony, Minwalla, Wiseman

deconfinement phase

4dYM

GR

3. confinement/deconfinement transition in holographic QCD

AdS D4 soliton Black D4 solution

4d pure YM

confinement phase

confinement/deconfinement transition

deconfinement phase

IIA SUGRA Scherk-Schwarz transition

There are additional evidences which support this disagreement.

Aharony, Sonnenschein, Yankielowicz 2006

Aharony, Minwalla, Wiseman

Mandal, T.M. 2011

◆ Does not work…

◆ Holographic construction of “4d pure Yang-Mills”Witten 1998, AGMOO 1999

confinement/deconfinement transition

4 dim SU(N) YM ← 5dim SU(N) SYM = N D4 brane Scherk-Schwarz mechanism

D4 soliton/black D4 transition

1. Introduction

2. Review of holographic QCD

3. Problem of the previous interpretation of the C/D transition

4. Our proposal

5. Conclusion

Plan of my talk

Sec.2

Sec.3Sec.4

D4 soliton/D3 soliton transition

In finite temperature case, we need to fix the boundary condition of the fermion along

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

4. Our proposal

In previous studies, people used the AP boundary condition

as in the standard thermodynamics.

It is not necessary since there is no fermion in 4d YM.

fermions are decoupled.

4d limit

It is valuable to test what does happen in the periodic (P) boundary condition along

.

Mandal, T.M. work in progress

AP b.c.:

P b.c.:

AdS D4 soliton OK

Black D4 solution NG

◆ Possible solution in the P boundary condition along

4. Our proposal

Mandal, T.M. work in progress

fermion has to be anti-periodic around the cigar geometry.

◆ Phase structure of 5dSYM in the periodic boundary condition

4dYM

AdS D4 soliton

IIA SUGRA

GL transition

confinement phasedeconfinement phase confinement/deconfinement phase transition in 4dYM.

4. Our proposal

Mandal, T.M. work in progress

localized D3 soliton

IIB SUGRA

We find a GL transition which may continue to

the confinement/deconfinement transition in 4dYM.

4dYM

GR?

◆ Phase structure of the 5dSYM

4dYM

AdS D4 soliton

Black D4

IIA SUGRA

SS transition

A transition obtained from

guess

Aharony, Sonnenschein, Yankielowicz 2006

Aharony, Minwalla, Wiseman

deconfinement phase

4dYM

GR

confinement phase

confinement/deconfinement phase transition in 4dYM.

4. Our proposal

Mandal, T.M. work in progress

◆ Phase structure of 5dSYM in the periodic boundary condition

4dYM

AdS D4 soliton

IIA SUGRA

GL transition

confinement phasedeconfinement phase confinement/deconfinement phase transition in 4dYM.

4. Our proposal

Mandal, T.M. work in progress

localized D3 soliton

IIB SUGRA

We find a GL transition which may continue to

the confinement/deconfinement transition in 4dYM.

4dYM

GR?

◆ Gregory-Laflamme (GL) transition in the P boundary condition.

4. Our proposal

Mandal, T.M. work in progress

AdS D4 soliton in IIA SUGRA

smeared D3 soliton in IIB SUGRA

Winding modes along are excited.

IIA Gravity description is invalid.

D3 brane

N D3 branes are uniformly distributed.

localized D3 soliton

N D3 branes are localized.

N D4 brane

Gregory-Laflamm (GL)

transition

AdS D4 soliton (smeared D3) vs localized D3 soliton

4. Our proposal

Mandal, T.M. work in progress

GL transition

IIA/IIB SUGRA

confinement phase vs deconfinement phase

a confinement/deconfinement transition

4d pure YM

We can observe the similarities between them.

◆ Phase structure of 5dSYM in the periodic boundary condition

4dYM

AdS D4 soliton

IIA SUGRA

GL transition

confinement phasedeconfinement phase confinement/deconfinement phase transition in 4dYM.

4. Our proposal

Mandal, T.M. work in progress

localized D3 soliton

IIB SUGRA

?

4dYM

GR

The GL transition may be connected to

the confinement/deconfinement transition in 4dYM.

◆ GL and Hagedorn transition.

4. Our proposal

Mandal, T.M. work in progress

GL instability

in IIB SUGRA

unstable KK mode along

Winding instability

in IIA string

unstable winding mode along

unstable QCD string winding

cf. Atick-Witten

4d limit

confinement/deconfinement transition

= Hagedorn instability in 4d YM

IIB IIA

◆ GL and Hagedorn transition.

4. Our proposal

Mandal, T.M. work in progress

GL instability

in IIB SUGRA

unstable KK mode along

Winding instability

in IIA string

unstable winding mode along

unstable QCD string winding

cf. Atick-Witten

4d limit

confinement/deconfinement transition

= Hagedorn instability in 4d YM

IIB IIA

The winding instability of the IIA string

may continue to that of the QCD string.

• We proposed that the GL may be related to the confinement/deconfinement transition.

• We can generalize our study to the d dimensional YM theory in general.

• This correspondence is consistent with the phase structure of the weakly coupled

lower dimensional gauge theory . (Tomorrow talk by G. Mandal)

• We can explain the chiral symmetry restoration/breaking transition in Sakai-Sugimoto model

through the same fashion.

Future Problems• Real time formalism. Does viscosity change?

• Understanding of the AP boundary condition case. 0B SUGRA

Conclusion

4d limit

AP b.c.:

P b.c.:

?

chiral symmetry restoration in Sakai-Sugimoto model

chiral symmetry restoration in Sakai-Sugimoto model

T-dual on the t-circle

chiral symmetry restoration in Sakai-Sugimoto model