Sang-Jin Sin (Hanyang Univ.)2007.8.23 @Cambridge
Based on Archive: 0707.2719
Nf/Nc ~ 1 in QCD. Since Nc has to be large for AdS/CFT, so is
the N_f. Then gravity back reaction is not an option but an essential.
The probe approximation gives typical phase diagram that is openwhile QCD phase
diagram is closed. (Kim,Lee,Nam,Park,Sin:0706.2525 ) back reaction closes phase diagram.
Baryon chemical potential and charge AdS charged black hole and R-charge Bulk Filling Branes and AdS black hole
Phase diagram closes Minkowski v.s Black hole Embeddings
(Baryon v.s Quark phase)
Baryon is not adjoint Rep. So it is not an Bulk Field. Chemical potential in 4d is a tail of A_0 Suggested to be tail of BRANE-FIELD A_0
by Kim-Sin-Zahed (hep-th/0608046)vector domination determines A_0=mu*psi_v
Horigome-Tanii (hep-th/0608198)Use eq. of Motion for A_0 without source
Nakamura, Seo, Sin, Yogendran:( with source
How to understand from Top down? Consider AdS5 filled with probe branes that fills
the whole Space Truncate DBI to quadratic F^2 if m_q=0, Induced metric => Bulk metric If m_q is not 0, there is deformation
Horizon
Boundary
ADS5 bulkBulk filling Brane
It is a brane U(1) charge Hoever, Brane is filling entire AdS 5 Hence it is a bulk charge as well. There is a Unique way a U(1) charge can
couple to the metric. Therefore U(1)_B charge must be related to
the charge parameter in RN black hole.
Chamblin et.al hep-th/9902170:
Q identified as R charge
Bulk field A sourced by Adjoint representation
What if Bulk=Brane?
Q=given baryon charge, q=parameter of RN BH What is relation of q & Q?
ANS:
The only information I used from the Brane language is the relation
NcNf is common to all Dp. 1/4pi^2 is for D7.
Fixed chemical potential (grand canonical)
• Fixed charge (Canonical) : add a surface term = or Legendre transform
•Equivalent physics // grand canonical
Introducing hard wallHawking-Page Transition (Herzog)
High temperature: charged ads BH Low temperature:
many different candidate: AdS, extremal charged BH, AdS with charges at the wall
We choose the last one for fixed charge case
Treat the grand canonical as Legendre Tr.
With back reaction v.s Without
Main change is attributed to the def. change of T.
Z. Fodor, S.D. Katz (hep-lat/0106002)
1. We seem to have phase diagram that mimic that of QCD.
2. We seems to have correct formalism to include the baryon density in bottom up approach.
3. How mass and chiral condensation, coupling etc. are running in density?
UNDER PROgress.
D3/D7 temperature ads Black holeBlack hole embedding v.s Minkoswki brane
Can there be a Minkowski Embedding? Kobayashi + et.al: (hep-th/0611099)claimed that there is no ME.
If we introduce only quarks: Yes. But If we introduce the baryon source,we may have ME.
(S. Nakamura, Seo, Sin, Yogendran)
String is connecting D7 and horizon
D7 brane deformation with spiky structure.
D7Spiky D7 stringquark
BH
Black hole Embedding with charge
BH
Baryon vertex
Minkowsky Embedding with charge
String is connecting D7 and baryon vertex
D7 brane deformation without spiky structure. = ME brane
Minkowski brane can exist even in the presence of charge. (Baryon vertex can be in contact with probe brane.)
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