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.)