Holographic QCD in Dense Medium and Nuclear Symmetry Energy Sang-Jin Sin (Hanyang Univ. ) 2011.5.25@cquest
QCD is one of greatest puzzles 20 century left for 21 century physicists. Due to the lack of understanding QCD, nuclear physics has been difficult and unclear
Two issues of this talk 1. Nuclear symmetry energy and koria 2. Two puzzles in hqcd. Chiral condensation in density plot T dependence of hadron physics in hqcd
Youngman Kim, Yunseok Seo, Ik Jae Shin, SJS arxiv:1011.0868 1st issue Nuclear symmetry energy A window to NEW-clear physics?
What is nuclear physics?
Valley of stability: Pauli v.s Coulomb the valley moves as we change the density and T
Symmetry Energy Liquid Drop Model Bethe-Weizsäcker formula (1935): It determines the curvature of valley of Stability.
Es and Pauli principle Asymmetry term Es(N-Z)^2 is the consequence of Pauli principle. Pauli term
Es(N-Z)^2 : If Es 0, pure neutron star is possible. If Es infinity: N=P
Importance of Es Structure of Neutron Star the mass and width of neutron-star crusts. Properties of Exotic Nuclei Nucleo-Synthesis during the supernova explosion.
non-interacting fermi gas? Non-relativistic Relativistic
Contribution of Pot.
What is known for? Little is known for high density. not Exp. nor theoretical.
Even for the low density The separation of free part and potential part may not be valid. So both low as well as high density regime is to be trusted.
Why difficult? 1. Strongly interacting. No good calculational tool in this regime. 2. Density effect: Even lattice qcd does not help much.
Holographic QCD Gluon dynamics Geometry. Confinement or deconfinement depends on geometry. Flavor dynamics by classical fields in warped geometry.
Basic picture Quark: Bifundamental, D6 D4 Meson: adjoint Dynamics: Dirac-Born-Infeld action Baryon: compact D5
A model for nuclear dense matter system: D4/D6 +cd4 Nc D4 provide Gluonic gravity background with confinement. One compactification x4. D4 baryon vertex. 2 flavor probe brane.
A Confining metric
Dynamics of probe barne DBI action: S= Density charge of F, fixed charge Legendre transformation.
DBI to Hamiltonian Hamiltonian of baryon vertex D4 Hamiltonian of baryon vertex D4
Force balance between D4 D6
Main idea: asymmetry in Z-N that in Q1-Q2
Result arxiv:1011.0868 Y.Kim, Y.Seo, I. Shin, SJS stiffness
Why analytic expression for symmetry energy. For the flat embedding approximation. Have confidence on
Dispersion relation for non-fermi-liquid
Why interesting? The anomalous dispersion relation is closely related to the fermi surface structure. For strongly interacting system, fermi surface is fuzzy and its implication is a big and interesting issue. Entire Thermodynamics as well as hydrodynamics of the strongly interacting Non-fermi liquid system will be a hot issue.
Non-fermi Liquid in Nuclear system? Liu et. al 0903.2477 0907.2694 If we choose we get
How to detect Es? Asymmetry in N-P is ~ that in π- π+ π-/π+ yields are sensitive to the stiffness of the symmetry energy near threshold energy. 29
Experiment 40 Ca+ 40 Ca, 96 Ru+ 96 Ru, 96 Zr+ 96 Zr and 197 Au+ 197 Au, and also plotted the ratios of N/Z and (N/Z) 2 as a function of N/Z at incident energy 0.4A GeV and 1.5A GeV, respectively.
Pauli principle in hqcd. Driving force of Z=N is Pauli principle Dual of fermion number is the local U(1) in 5d. Coulomb repulsion of the dual E&M is responsible for the Es.
Conclusion I Symmetry Energy can be calculated using the holographic principle. Physics of fermi surface for strongly interacting system including Non-standard dispersion relation will lead us new and interesting aspect of nuclear matter: It is non-fermi Liquid!
Bogeun Gwak, Minkyoo Kim, Bum-Hoon Lee, Yunseok Seo, SJS arxiv:1105.2872 2 nd Issue. Holographic chiral condensation and Temperature dependence of Hadron physics.
Two puzzles in hqcd Temperature dependence of physical quantity in Confined phase. Chiral condensation increases with density, which is opposite to the field theory expectation.
The origin of puzzle Hawking Page transition. When there is a scale other than the temperature, there are competing geometries. (Ex: adsbh v.s thermal ads) The geometry for the Low temperature phase does not have any temperature dependence.
To overcome this difficulty. One should think about geometry that does not allow any HP transition: For example Black D3 geometry without compactification or hardwall. Question is how to obtain confinement, which need a scale! And a scale means HP!
Hadrons without confined gluons possibility that there is no gluon confinement nevertheless hadrons are allowed. Baryons as well as Mesons!
Mesons and baryons in the black hole phase. For the meson, it is known to exist in the black hole phase unless there are free quarks. This is due to the presence of the black hole embeddings. However, usually the baryons are allowed simply because compact D5 (Witten baryon vertex) can not be sustained in the sky of the black hole.
The idea is to introduce D-instanton charge q Its effect to metric is just overall mutiplication by a dilaton factor No effect in Einstein frame. Its contribution to the action is also 0 due to the cancelation between dilaton and axion. Therefore NO geometric phase transition!
geometry
Character of geometry is Pseudo confinement Wilson loop is to be calculated in the string frame there is effects of q. : i) confinement at 0 temperature. at large enough separation, ii) linear potential before critical separation where it is screened.
Why baryons exist? D-brane dynamics is given by DBI action which has dilaton factor. Also it is calculated in the string metric. So it is affected by the presence of q. BV allowed due to the repulsion between D-1 /D5
q allows baryon!
Chiral dynamics q dependence of chiral condensation is consistent with field theory result.
Geometric understanding of chiral dynamics
Chiral symmetry breaking in quark phase
Understanding the chiral condensation plot
Baryon Phase : chiral symmetry is always broken
Density plot of chiral condensation
Phase diagram
Conclusion II This is the First model with correct chiral symmetry breaking pattern. All the bottom model so far shows the opposite behavior. Assuming Tc for x-b > Tc for deconf. This is realistic. We can have temperature dependence in hadron phase.