Holographic Hadrons in dense medium Sang-Jin Sin

Maldacena Phenomena A legend in our generation hep-th/ Adv.Theor.Math.Phys.2: ,1998 The Large N limit of super conformal field theories and super-gravity. Juan Martin Maldacena, Cited 6634 times Juan Martin Maldacena, Cited Weinberg model : cited 7000 times for 40 years Kyoto 2

Why? Ads/cft seems to connect string theory to many other branches of physics like *QCD, *CMT, Including QHE, High Tc SC, Graphene Not difficult to predict what will happen next 10 years! Kyoto 3

Defect and hope Large N, 4 SUSY, Extra degree of freedom…… Far from the reality. Nevertheless ….. After 35 years of qcd, strong interaction regime is still in mystery. Any field theory calculation is casted by doubt. Asymptotic freedom is not useful at all for the nuclear physics. Hope is overwhelming the Difference at this moment Kyoto 4

Origin: D-brane Kyoto pictures by Gubser 5

Ads & RN Black hole Kyoto pictures by S. Gubser 6

Phase diagram of qcd Kyoto 7

Motive from Heavy Ion collision Kyoto 8 Deconfined. Original degree of freedom of qcd. But experiment shows still strongly interacting. perfect theoretical setting for ads/qcd

Heavy ion collision Kyoto 9

Elliptic flow,perfect fluidity, sqgp Kyoto 1010

Finite Temperature  BH Kyoto 11

Expanding QGP and Elliptic Flow (Nakamura, Kim, SJS 2006) Kyoto 1212

Difficulties for Hadrons Need New effective degrees of freedom Emergence of a Scale: Lambda QCD what caused it? Gluon condensation? Confinement Chiral symmetry breaking Kyoto 1313

Confinement. scale Need a scale of scale inv. Theory (qcd) MIT bag-Model In ads/qcd, 1. Hard wall ads/cft  discrete glueball spectrum 2. Witten bubble : double wick rotation of BH  area law Kyoto 1414

Evidence for confining metric Wilson Loop : Area law? Yes for both. (for pure N=4 YM, Coulomb) Polyakovloop : Zero ? Yes Appearance of scale: in qcd: T and very different In hqcd: integration constant. T and equal putting Kyoto 1515

Adding Matter with probe brane Kyoto 1616

Baryon Chemical potential Global symmetry Boundary AdS/CFT gauge symmetry Bulk Local charge Kyoto 17

Pauli in AdS 1. Classical Physics does not encode fermi-statistics. We are dealing with QM system. 2. In boundary we have global U(1) Q. We have a local Coulomb repulsion in AdS. What is its dual in boundary? Suggestion: Dual of the local repulsion is the Pauli effect. A classical realization of quantum statistics. Evidence: i. RN AdS shows fermionicC_v =a T. (Zahed,sjs) ii. Baryon Density dependence of the free energy. (Zahed,sjs) iii. Brane dynamics for strange matter (Y.Kim. Y.Seo. Sjs) Kyoto 1818

Chemical potential with Baryon Kyoto How mesons behave on this configuration? 1919

Holographic Hadrons in a Confining Finite Density Medium ( ) Y. Seo, J. Shock, D. Zoakos +SJS Consider the situation where confinement, gluon condensation, finite baryon density are implemented. But T=0. Ask how the meson/baryon spectrum depends on the density? Kyoto 2020

Background geometry Kyoto Gubser’s background Non supersymetric extension of D3-D(-1) bound system Supersymmetry and chiral symmetry is broken r 0 is proportional to the gluon condensation in gauge theory This geometry support confining phase 2121

D7 embedding Kyoto 2222

Shape of Baryon vertex Kyoto  D5 brane solution  Force at cusp D4/D6(D3/D5) YS, S Sin, JHEP 0804:010,

Interaction of D7-D5: force balance with Baryon vertex Kyoto (Baryon D5 + F1’s +probe D7) can be stationary if Force balance condition is fulfilled 2424

Kyoto 2525

Baryon mass with density Kyoto  Deformation of D-brane Deformation of D5 braneBaryon mass Deformation of D7 braneBaryon-baryon interaction  Density dependence of baryon mass 2626

Meson: Fluctuation on D7 brane Scalar fluctuation Kyoto Second order Lagranian with quardratic terms for fluctuation Equation of motion for fluctuation 2727

Fluctuation on D7 brane By using shooting method, we can calculate mass spectrum of fluctuation, which is meson. For large enough quark mass, meson mass decreases! In such case BR-scaling exist Kyoto 2828

For very small quark mass: Kyoto 2929

Chiral symmetry breaking In top down: chiral condensation is probe brane’s tail curvature in mass direction. Even for the U(1) chiral symmetry as a rotation, it is impossible to restore it by density. For non-abelian chiral symmetry  SS model, 1. v. hard to treat chiral-condensation itself. if not impossible. No room to allow mass. 2. chiral and deconfinement transition for max. separ. Here, we use bottom up (EKSS) with gravity back reaction included Kyoto 3030

Analogy: h-superconductor Kyoto 3131

Abelian higgs in ads Couple the abelian higgs model to gravity. Set zero potential apart from the mass term determined by the conformal dimension of the excitations Kyoto 3232

Condensation Kyoto 3333

[S.C v.s Chiral] transition Supersonducting  Normal state BH with scalar hair  BH without hair Question: Can we discuss chiral transition using similar idea? Yes. We can. Star v.s BH transition Kyoto 3434

Set up Kyoto 3535

Boundary conditions Kyoto 3636

Numerical results (Y.Ko+sjs) Kyoto 3737

What next? Here, we studied Density dependences. Following objects are calculable in hqcd: 0.Phasediagram (not critical point/crossover). 1. equation of state. 2. all Thermodnamic quantities. 3. condensations (chiral and gluon meson … ) 4. susceptiblities 5. spectral functions. 6. Symmetry energies. 7. Differnet models and Different modes. Etc …… Kyoto 3838

Conclusion AdS/CFT connects string theory to many other branch of physics especially qcd. dense matter theory in qcd by ads/cft is especially useful since the correspondence is most clear and not much has been done in lattice Kyoto 3939