Bulk Filling Branes and gravity backreaction to Baryon

Bulk Filling Branes and gravity backreaction to Baryon Density Sang-Jin Sin (Hanyang Univ. ) 2007. 8. 23 @Cambridge Based on Archive: 0707. 2719

Motive: Phase diagram of Baryon density � Nf/Nc ~ 1 in QCD. � Since Nc has to be large for Ad. S/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 open while QCD phase diagram is closed. (Kim, Lee, Nam, Park, Sin: 0706. 2525 ) � back reaction closes phase diagram.

Plan of the talk � Baryon chemical potential and charge � Ad. S charged black hole and R-charge � Bulk Filling Branes and Ad. S black hole Phase diagram closes � Minkowski v. s Black hole Embeddings (Baryon v. s Quark phase)

Baryon chemical potential � Baryon is not adjoint Rep. � So it is not an Bulk Field. � Chemical potential in 4 d 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

Bottom Up Approach � How to understand from Top down? � Consider Ad. S 5 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 Boundary Bulk filling Brane ADS 5 bulk Horizon

How baryon charge appear? � It is a brane U(1) charge � Hoever, Brane is filling entire Ad. S 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.

Ad. S charged black hole Chamblin et. al hep-th/9902170: Q identified as R charge Bulk field A sourced by Adjoint representation What if Bulk=Brane?

Back reaction of metric � Q=given baryon charge, q=parameter of RN BH � What is relation of q & Q? � ANS:

Remark � The only information I used from the Brane language is the relation � Nc. Nf is common to all Dp. � 1/4 pi^2 is for D 7.

Thermodynamics without Hard Wall � Fixed chemical potential (grand canonical) • Fixed charge (Canonical) : add a surface term = or Legendre transform • Equivalent physics // grand canonical

Phase transitions without/with back reaction � Introducing hard wall Hawking-Page Transition (Herzog) � High temperature: charged ads BH � Low temperature: many different candidate: Ad. S, extremal charged BH, Ad. S with charges at the wall � We choose the last one for fixed charge case � Treat the grand canonical as Legendre Tr.

Phase diagram (fixed density) � With back reaction v. s Without Main change is attributed to the def. change of T.

Phase diagram: chemical potential Z. Fodor, S. D. Katz (hep-lat/0106002)

Temperature along the phase boundary

conclusion 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.

Brane Embeddings D 3/D 7 temperature ads Black hole embedding v. s Minkoswki brane

Some Issue in D 3/D 7 with baryon charge � 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)

Quark Phase (D 3/D 7) � String is connecting D 7 and horizon � D 7 brane deformation with spiky structure. D 7 Spiky D 7 string quark BH Black hole Embedding with charge

Baryon Phase of D 3/D 7 String is connecting D 7 and baryon vertex D 7 brane deformation without spiky structure. = ME brane Baryon vertex BH Minkowsky Embedding with charge

Conclusion II � Minkowski brane can exist even in the presence of charge. (Baryon vertex can be in contact with probe brane. )