Some Issues in AdS/QCD Based on collaboration with Sang-Jin Sin (Hanyang Univ.) 2007.11.30 @HYU Based on collaboration with S.Nakamura, YS.Seo, P.Yogendran (Hanyang,cquest) BH.Lee, YM.Kim, CY.Park (Cquest, KIAS) E.Shuryak, I.Zahed, KY.Kim (Stony Brook)
String Theory and Hadron physics Invented as a Hadron theory (1GeV) Became theory of gravity (plank scale) back to Hadron theory with AdS/CFT Key idea: D-brane , Open-Closed string duality(gauge/gravity) Decoupling of Plank scale: New scale =AdS radius t`Hooft coupling of gauge theory.
D-brane Open string gauge theory Closed string gravity D-brane=Membrane like closed string soliton whose vibration is restricted as open string vibration.
YM/AdS and Thermal YM / AdS-BH P 5d AdS 4d YM
Quarks, baryons, chemical potentials mu=A at infinity D3 F1 Nf Nc D5 Quark=string connecting color & flavor branes Baryon vertex Chemical potential= tail of electricpotential
A few questions in RHIC//AdS Jet quenching (with I. Zahed 2004) Elliptic Flow (with S.Nakamura & SP. Kim,06) Cooling and Expansion Rate (Shuryak & Zahed,05) Calculation of dissipation in expanding Fireball (with KY.Kim & Zahed, 07) Dense matter effect and Phase diagram (with Nakamura, Seo, Yogendran, 06) Rapid thermalization
In the rest of this talk I will pick up one issue and give some details . Phase diagram in Temperature-Density plane Back reaction of geometry to the dense matter is essential. With and only with BR, Phase diagram closes
Deconfinement Phase Transition 1. Without Matter: Hawking Page Transition between Two competing geometries: AdS with IR cutoff (Low T) & AdS BH (High T) 2. what if there is baryon chage?
Problem in Probe brane description Large Nc and finite Nf: little effect of baryon/quark density in phase transition and P.D is OPEN Nf/Nc=finite T Nf confinement density
Origin of the problem Nf/Nc ~ 1 in QCD. Since Nc has to be large for AdS/CFT, so is the Nf. Then gravity back reaction is not an option but an essential. back reaction closes phase diagram.
Baryon chemical potential Baryon is not adjoint Rep. not a Bulk Field. Chemical potential in 4d is a constant A0. Therefore mu= Tail of BRANE-FIELD A0. (Kim-Sin-Zahed : hep-th/0608046) Horigome-Tanii (hep-th/0608198) Use eq. of Motion for A_0 mu=A at infinity
How baryon charge appear? a brane U(1) charge If Brane is Filling entire AdS 5 brane charge= bulk charge. Since there is a unique way a U(1) charge can couple to the metric, U(1)_B charge must be related to the charge parameter in RN black hole.
AdS charged black hole Chamblin et.al hep-th/9902170: Q identified as R charge Bulk field A sourced by Adjoint representation Bulk=Brane R charge and Q play the same role
Back reaction of metric Q=given baryon charge, q=parameter of RN BH What is relation of q & Q? ANS:
Thermodynamics without Hard Wall Fixed chemical potential (grand canonical) Fixed charge (Canonical) : add a surface term or Legendre transform grand canonical v.s Canonical
Phase transitions without/with back reaction Introducing hard wallHawking-Page Transition (Herzog) High temperature: charged ads BH Low temperature: AdS with charges at the wall for fixed charge case Treat the grand canonical as Legendre Tr. Of canonical case.
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.