based on arXiv:1107.4048 (to appear in JHEP) with G. Mandal (Tata Institute in India)

based on arXiv:1107.4048 (to appear in JHEP)

with G. Mandal (Tata Institute in India)

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

confinement phase

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

AdS D4 soliton

4 dim SU(N) YM IIA SUGRA

1. Introduction

confinement phase

AdS D4 soliton

AGMOO 1999

deconfinement phase

black D4 solution

Finite temperature

This identification was widely believed and employed in many studies.

1. Introduction

confinement phase

AdS D4 soliton

AGMOO 1999

deconfinement phase

black D4 solution

Finite temperature

Aharony, Sonnenschein, Yankielowicz 2006

Aharony, Minwalla, Wiseman

Mandal, T.M. 2011

Several problems have been reported

in this identification.

1. Introduction

confinement phase

AdS D4 soliton

AGMOO 1999

deconfinement phase

black D4 solution

Finite temperature

Mandal, T.M. 2011

localized D3 solution

confinement phase

AdS D4 soliton

AGMOO 1999

deconfinement phase

black D4 solution

Finite temperature

Mandal, T.M. 2011

Plan of my talk

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

AdS D4 soliton

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

◆ Phase structure of 5dSYM on

(Witten 1998)

one-loop

5d SYM on 4d pure YM

: suppression of the loops

from KK modes

: temperature ≪ KK scale

4d limit

(Witten 1998)

AdS D4 soliton

This geometry describes the strong coupling 5d SYM in the low temperature regime.

AdS D4 soliton

◆ Phase structure of 5dSYM on

◆ Holographic pure YM (Holographic QCD)

(Witten 1998)

AdS D4 soliton

By using some prescription, we can extrapolate the information of the confinement phase of

the 4d YM through the AdS D4 soliton. The results obtained from the extrapolation agree with

lattice and experiments qualitatively and sometimes even quantitatively. (e.g. Sakai-Sugimoto model)

(Witten 1998)

AdS D4 soliton

It is natural to explore a higher temperature regime to find similar relation.

•What is the gravity dual of the deconfinement phase?

•What is the gravity dual of the confinement/deconfinement transition?

◆ Holographic pure YM (Holographic QCD)

confinement phase

AdS D4 soliton

AGMOO 1999

deconfinement phase

black D4 solution

Finite temperature

Mandal, T.M. 2011

Plan of my talk

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

◆ Previous set up for the finite temperature 4dYM.

: AP boundary condition for fermions

(Scherk-Schwarz circle)

→ mass → breaks supersymmetry

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

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

In the previous studies, people used the AP boundary condition along

as in the standard thermodynamics.

The system has a

AdS D4 soliton

Black D4

IIA SUGRA

confinement phasedeconfinement phase

◆ Phase structure of 5dSYM on with (AP,AP) B.C.

Black D4 braneAdS D4 soliton

AdS D4 soliton

Black D4

IIA SUGRA

confinement phase

deconfinement phase

A: C:•confinement phase

•AdS D4 soliton

•deconfinement phase

•Black D4

center symmetry of the SU(N)

(order parameter of the C/D transition)

AdS D4 soliton

Black D4

IIA SUGRA

confinement phase

deconfinement phase

center symmetry of the SU(N)

(order parameter of the C/D transition)

A: C:•confinement phase

•AdS D4 soliton

•Black D4

This conjecture is not correct!

AdS D4 soliton

Black D4

IIA SUGRA

confinement phase

A transition obtained from

Mandal, T.M. 2011deconfinement phase

B: C’:•confinement phase

•AdS D4 soliton

•Black D4•deconfinement phase

confinement phase

AdS D4 soliton

AGMOO 1999

deconfinement phase

black D4 solution

Finite temperature

Mandal, T.M. 2011

Plan of my talk

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.

This AP boundary condition is not necessary to obtain

the thermal partition function of the 4d YM, in which no fermion exists.

fermions are decoupled.

4d limit

It is valuable to investigate what will happen in the periodic (P) boundary condition along

Mandal, T.M. 2011

AP b.c.:

P b.c.:

◆ Phase structure of 5dSYM on with (P,AP) B.C.

AdS D4 soliton

IIA SUGRA

GL transition

4. Our proposal

localized D3 soliton

IIB SUGRA 4dYM

Mandal, T.M. 2011

New solution!

•confinement phase

•AdS D4 soliton

•Localized D3 solitoncf. Aharony, Marsano, Minwalla, Wiseman 2004,

Harmark, Obers 2004

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

4. Our proposal

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.

N D3 branes are localized.

N D4 brane

Gregory-Laflamm (GL)

transition

Mandal, T.M. 2011

◆ Phase structure of 5dSYM on with (P,AP) B.C.

AdS D4 soliton

(= smeard D3 brane in IIB)

IIA SUGRA

GL transition

4. Our proposal

IIB SUGRA

We find that the GL transition may continue to

the confinement/deconfinement transition in 4dYM.

Mandal, T.M. 2011

◆ GL and Hagedorn transition.

4. Our proposal

GL instability

in IIB SUGRA

momentum instability along

Winding instability

in IIA string

unstable winding mode along

unstable QCD string winding

cf. Atick-Witten

confinement/deconfinement transition

= Hagedorn instability in 4d YM

IIB IIA

Mandal, T.M. 2011

4d limit

(weak coupling)

◆ GL and Hagedorn transition.

4. Our proposal

GL instability

in IIB SUGRA

Winding instability

in IIA string

unstable winding mode along

unstable QCD string winding

cf. Atick-Witten

4d limit

(weak coupling)

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.

Mandal, T.M. 2011

momentum instability along

•We proposed the following new correspondence in the holographic QCD.

• Chiral symmetry restoration/breaking transition in the Sakai-Sugimoto model

by using our new correspondence. (Manda, T.M 2011)

• Gauge theory analysis of the C/D transition in some special cases is possible and

confirmed the relation to the GL transition. (Mandal, Mahato, T.M. 2009, Mandal, T.M. 2011)

Future Direction

• Real time formalism. Does the universal viscosity ratio change? (No black brane appears in our proposal!)

Conclusions

We have shown the following things also…

4 dim SU(N) YM IIA/IIB SUGRA• confinement phase

• deconfinement phase

• C/D transition

• unstable QCD string wrapping

• AdS D4 soliton (= smeard D3 soliton)

• localized D3 soliton in IIB

• Gregory-Laflamm transition in IIB

• unstable IIA string wrapping (= unstable KK mode along )

•We proposed the following new correspondence in the holographic QCD.

• Chiral symmetry restoration/breaking transition in the Sakai-Sugimoto model

by using our new correspondence. (Manda, T.M 2011)

• Gauge theory analysis of the C/D transition in some special cases is possible and

confirmed the relation to the GL transition. (Mandal, Mahato, T.M. 2009, Mandal, T.M. 2011)

Future Direction

• Real time formalism. Does the universal viscosity ratio change? (No black brane appears in our proposal!)

Conclusions

We have shown the following things also…

4 dim SU(N) YM IIA/IIB SUGRA• confinement phase

• deconfinement phase

• C/D transition

• unstable QCD string wrapping

• AdS D4 soliton (= smeard D3 soliton)

• localized D3 soliton in IIB

• Gregory-Laflamm transition in IIB

• unstable IIA string wrapping (= unstable KK mode along )

Thanks!

based on arXiv:1107.4048 (to appear in JHEP) with G. Mandal (Tata Institute in India)

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