based on arxiv:1107.xxxx with g. mandal (tifr) what is the gravity dual of the...
TRANSCRIPT
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.:
?