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based on arXiv:1107.xxxx with G. Mandal (TIFR) What is the gravity dual of the confinement/deconfinement transportation in holographic QCD Takeshi Morita University of Crete

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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 Several problems have been reported in this identification.

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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 D4 soliton/D3 soliton transition Aharony, Sonnenschein, Yankielowicz 2006 Aharony, Minwalla, Wiseman Mandal, T.M Several problems have been reported in this identification.

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◆ 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.3 Sec.4 D4 soliton/D3 soliton transition

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2. Review of holographic QCD (Witten 1998) : anti-periodic (AP) boundary condition for fermions (Scherk-Schwarz circle) → mass → breaks supersymmetry (0)123(4)56789 D 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

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2. Review of holographic QCD ◆ Holographic 4d pure YM IIA SUGRA 5d SYM on 4d pure YM Important point Gravity 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)

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2. Review of holographic QCD IIA SUGRA 5d SYM on 4d pure YM Important point Gravity 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

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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

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◆ 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.3 Sec.4 D4 soliton/D3 soliton transition

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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)123(4)56789 D 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

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

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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 YM SS transition at We can observe the similarities between them.

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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?

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◆ 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

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◆ 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

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◆ 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

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◆ 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

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◆ 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

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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 ◆ Does not work…

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◆ 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.3 Sec.4 D4 soliton/D3 soliton transition

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In finite temperature case, we need to fix the boundary condition of the fermion along (0)123(4)56789 D 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.:

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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.

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◆ Phase structure of 5dSYM in the periodic boundary condition 4dYM AdS D4 soliton IIA SUGRA GL transition confinement phase deconfinement 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 ?

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◆ 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

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◆ Phase structure of 5dSYM in the periodic boundary condition 4dYM AdS D4 soliton IIA SUGRA GL transition confinement phase deconfinement 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 ?

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◆ 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

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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.

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◆ Phase structure of 5dSYM in the periodic boundary condition 4dYM AdS D4 soliton IIA SUGRA GL transition confinement phase deconfinement 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.

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◆ 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

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◆ 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.

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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.: ?

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chiral symmetry restoration in Sakai-Sugimoto model

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T-dual on the t-circle

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chiral symmetry restoration in Sakai-Sugimoto model

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