based on arXiv:1107.4048 (to appear in JHEP) with G. Mandal (Tata Institute in India)
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Transcript of 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
◆ 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
AGMOO 1999
deconfinement phase
black D4 solution
Finite temperature
This identification was widely believed and employed in many studies.
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
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
◆ 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
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.
localized D3 solution
◆ 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
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.
localized D3 solution
Plan of my talk
Sec.2
Sec.3
Sec.4
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
4dYM
AdS D4 soliton
confinement phasedeconfinement phase confinement/deconfinement phase transition in 4dYM.
4dYM
◆ Phase structure of 5dSYM on
2. Review of holographic QCD
(Witten 1998)
?
?
??
?
?
one-loop
5d SYM on 4d pure YM
: suppression of the loops
from KK modes
: temperature ≪ KK scale
4d limit
4dYM
confinement phasedeconfinement phase confinement/deconfinement phase transition in 4dYM.
4dYM
GR
2. Review of holographic QCD
(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
4dYM
confinement phasedeconfinement phase confinement/deconfinement phase transition in 4dYM.
4dYM
GR
◆ Holographic pure YM (Holographic QCD)
2. Review of 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)
4dYM
confinement phasedeconfinement phase confinement/deconfinement phase transition in 4dYM.
4dYM
GR
2. Review of holographic QCD
(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)
◆ 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
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.
localized D3 solution
Plan of my talk
Sec.2
Sec.3
Sec.4
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
4dYM
AdS D4 soliton
Black D4
IIA SUGRA
confinement phasedeconfinement phase
4dYM
GR
3. Problem of the previous interpretation of the C/D transition
◆ Phase structure of 5dSYM on with (AP,AP) B.C.
Black D4 braneAdS D4 soliton
4dYM
AdS D4 soliton
Black D4
IIA SUGRA
confinement phase
Previous
conjecture
deconfinement phase
4dYM
GR
A
3. Problem of the previous interpretation of the C/D transition
◆ Phase structure of 5dSYM on with (AP,AP) B.C.
A: C:•confinement phase
•AdS D4 soliton
•deconfinement phase
•Black D4
C
center symmetry of the SU(N)
(order parameter of the C/D transition)
4dYM
AdS D4 soliton
Black D4
IIA SUGRA
confinement phase
Previous
conjecture
deconfinement phase
4dYM
GR
A
3. Problem of the previous interpretation of the C/D transition
◆ Phase structure of 5dSYM on with (AP,AP) B.C.
center symmetry of the SU(N)
(order parameter of the C/D transition)
A: C:•confinement phase
•AdS D4 soliton
•deconfinement phase
•Black D4
C
This conjecture is not correct!
4dYM
AdS D4 soliton
Black D4
IIA SUGRA
confinement phase
A transition obtained from
guess
Aharony, Sonnenschein, Yankielowicz 2006
Mandal, T.M. 2011deconfinement phase
4dYM
GR
A
BC’
A:
3. Problem of the previous interpretation of the C/D transition
◆ Phase structure of 5dSYM on with (AP,AP) B.C.
B: C’:•confinement phase
•AdS D4 soliton
•Black D4•deconfinement phase
◆ 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
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.
localized D3 solution
Plan of my talk
Sec.2
Sec.3
Sec.4
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.
4dYM
AdS D4 soliton
IIA SUGRA
GL transition
confinement phasedeconfinement phase confinement/deconfinement phase transition in 4dYM.
4. Our proposal
localized D3 soliton
IIB SUGRA 4dYM
GR?
A
B
Mandal, T.M. 2011
A: B:
New solution!
•confinement phase
•AdS D4 soliton
•deconfinement phase
•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.
localized D3 soliton
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.
4dYM
AdS D4 soliton
(= smeard D3 brane in IIB)
IIA SUGRA
GL transition
confinement phasedeconfinement phase confinement/deconfinement phase transition in 4dYM.
4. Our proposal
localized D3 soliton
IIB SUGRA
We find that the GL transition may continue to
the confinement/deconfinement transition in 4dYM.
4dYM
GR?
A
B
Mandal, T.M. 2011
A: B:
◆ 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!