Gauge/Gravity duality and Nuclear Symmetry energy

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Julia Skowrońska
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1 Gauge/Gravity duality and Nuclear Symmetry energy Sang-Jin Sin (Hanyang Univ. ) @USTC

2 Greeks called indivisible Building block of the universe Atom Two most basic questions in physics are 1. What is the Atom? 2. What Forces glue them together to make the visible world? 2

3 Modern Theory of Atom Dalton s story was not the end 3

4 Force=exchange of glue particles Two levels of strong force. (QCD,meson) Gravity is very special and not included here 4

5 QCD: today s theme For High E: g<<1: Asymptotic freedom 5

6 For Low E: QCD is still difficult interaction strong, fluctuation large High E v.s Low E of Strong int. For strong int. Not clear even what is particle 6

7 Asymptotic freedom and confinement 7

8 General Idea for strong int. Reformulate theory in terms of new degree of freedom whose interactions are weak. Duality 8

9 An idea from string theory Replace strong nuclear force by classical gravity(geometry). What is the string theory? 9

10 Old String theory Regge trajectory spectrum of string 10

11 Difficulty of old string theory Hard to explain the quark s free behavior. abandoned and re-incardnated as a quantum gravity, which is a BIG deal! Why? qm gravity is difficult! puzzle 11

12 Specialty of Quantum gravity Force = - grad (potential Energy) Einstein: gravity is not a force but a curvature. Curvature = k (Energy (mass)) Quantum fluctuation of any field generate infinite Energy infinite gravity essential difficulty 12

13 Origin of the vacuum energy Uncertainty principle. p x in a particle theory, any large energy is possible (Delta x 0) 13

14 Finiteness of String theory stringy uncertainty principle energy of the string per unit length is constant E up means length up Minimal length UV divergence disappear 14

15 Open closed duality Open String : gauge theory Theory of Matter Closed string: gravity Theory of space-time Two are dual to each other through D-brane: 15

16 Closed string soliton D-branes That this object has dual description by dynamics of open string ending on it, is the major discovery of 90. (Polchinski) vibration of D brane =The low energy dynamics SU(N) SYM =string theory at warped geometry. 16

17 D-brane & gravity Stack of D-brane space time warp due to the tension. (AdS). Eschers s Angels and devils" 17

18 AdS/CFT duality String in AdS5 is dual to SYM in 4d. 5d v.s 4d Holographic corr. For large coupling,, AdS/CFT gravity/gauge dualtiy 18

19 Consequence of duality Gluon dynamics is replaced by ads gravity. For large N_c, gravity is weakly coupled. Correlation function in 4d can be calculated by the classical dynamics at the ads bulk. 19

20 AdS/CFT at finite T 20

21 II. String theory in RHIC/LHC collider 21

22 Relativistic Heavy Ion Collider (Brookhaven N.L) Au-Au collision E~200 GeV/nucleon Seek quark-gluon plasma(qgp) 22

23 Detectors star phenix 23

24 Some Puzzles (my contributions) Elliptic flow (hep-th/ ) * Perfect fluid : ( , ) Jet quenching (hep-th/ ) Early thermalization (hep-th/ ) QGP is strongly interacting 24

25 Liquid than Gas 25

26 Jet-Quenching Energy Loss Problem. 26

27 Elliptic flow v 2 Interactions among the produced particles: Pressure gradients generate positive elliptic flow v 2 Early observation at RHIC: v 2 as large as predicted by perfect fluid dynamics! 27

28 Perfect fluid Exp: While perturbative evaluation ~1/g^4 ads/cft : Universal value 28

29 Transport Coeff. X.Ge, Y.Matsuo, F.Shu, SJS,Takuya Tsukioka, arxiv: Y. Matsuo, SJS. S.Takeuchi, T. Tsukioka, C.Yoo (APCTP), archiv: Linear response theory: causal Green function T.C Ads/cft can calculate <JJ>, <TT> easily. 29

30 III. String theory and Nuclear Symmetry Energy. There will be a heavy ion collider constructed in Korea in 5 year with ~billion dollar. 30

31 KoR(are)I(sotope)A

32 Valley of stability: Pauli v.s Coulomb

33 Symmetry Energy Liquid Drop Model Bethe-Weizsäcker formula (1935): E(ρ, α) E(ρ, 0) + S 2 (ρ) α 2, α (N Z)/A. It determines the curvature of valley of Stability.

34 Es and Pauli principle Asymmetry term Es(N-Z)^2 is the consequence of Pauli principle. Pauli term

35 Es(N-Z)^2 : If Es 0, pure neutron star is possible. If Es infinity: N=P

36 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.

37 non-interacting fermi gas E k = 3 5 (N p Fp + N n Fn ) E sym = F 3 ρ2/3 Non-relativistic ρ 1/3 Relativistic

38 ]. We f ourwill simulation always test results the to sensitivity differentof choices our simulation of results to different choices of density of the Isovector and momentum part of the dependence Equationof of the State Isovector of the Equation of State e We the EoS). potential will In the always part non-relativistic of the test symmetry the frame sensitivity energy, the potential of partour of the simulation symmetry energy, results to diffe (ρ), density [1]: and momentum dependence of the Isovector part of the Equ Contribution of Pot. o EoS). E sym = In E sym the (kin)+e non-relativistic sym (pot) ɛ F pot) ɛ F frame the potential part of the sym 3 + C sym(ρ) (3) 3 + C sym(ρ) (3) sted m(ρ), density by [1]: parametrizations employing three different of the symmetry density parametrizations of the symmetry ntials y increasing [1, 23, behaviour 38], one withadensity, rapidly roughly increasing behaviour with density, roughly E sym = E sym (kin)+e sym (pot) ɛ F ortional ne with ato linear ρ 2 (Asy increase superstiff), of the potential one with parta linear increase of the potential 3 + C sym(ρ) part e symmetry energy density Probing (Asy the stiff) Nuclear and Symmetry one with Energy a kind with of saturation Heavy Ion Collisions sy stiff) and one with a kind of saturation ndn tested decreasing normal by density at higher employing (Asydensities. soft), three even decreasing different at higher density densities. parametrizations of Inwith particular, the stronger for the density symmetry dependence, term with the stronger density dependence, entials [1, 23, 38], ( ) one 2/3 with a rapidly increasing behaviour with de 2(ρ/ρ ρ portional to ρ 2 2(ρ/ρ 0 ) 2 0 ) 2 E sym (ρ) =a (Asy + superstiff), b 1+(ρ/ρ ρ 0 1+(ρ/ρ 0 ), one with a linear increase (4) 0 ), (4) of the ing Symmetry the Nuclear Energy Symmetry with Heavy Energy Ionwith Collisions Heavy Ion Collisions 5 5 7the emev ρ 0 isymmetry (fixed the saturation by the kinetic energy density, contribution a=12.7 MeV density Eq.3) (fixed by (Asy the kinetic stiff) contribution andeq.3) one with a kind eb=19 erm he und ofsymmetry 31.7 with MeV, normal MeV weaker toterm. give The density with alinear saturation weaker dependence density (Asy density value dependence around of dependence soft), 31.7 MeV saturation even. The around linear decreasing saturation density dependence at higher densities ply given ( by: ) 2/3 ( ) In particular, ρ 2/3 (ρ) =a E for ( the ) sym (ρ) ρ ρ =a 819.1ρ 2/3 symmetry term with the stronger density depe ρ ρ 2, 819.1ρ 2, (6) ρ (6) 0 (ρ/ρ 0 ), E sym (ρ) =a ρ 0 + b ( (ρ/ρ 0 ), (5) ρ 2/3 ρ 2(ρ/ρ 0 ) 2 (5). e a=12.7 MeV. 0 The ameterizations three parameterizations cross E sym at(ρ) normal =a cross density at normal at thedensity empirically + b at the known empirically 1+(ρ/ρ 0 ), known Figure 1. Density dependence of the symmetry energies used oefficient ρ etry energy of the coefficient Bethe-Weizsäcker of Bethe-Weizsäcker formula. 0 As shown formula. in Fig.1 As shown the in Fig.1 the densities etry energy below at densities the normal below value theisnormal larger in value the is Asysoft larger case, in thewhile Asysoft case, while presented here: Asy-soft (solid) and Asy-stiff (dashed).

39 What is known for? Little is known for high density. not Exp. nor theoretical.

40 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.

41 Why difficult? 1. Strongly interacting. No good calculational tool in this regime. 2. Density effect: Even lattice qcd does not help much.

42 Repeat: String theory idea is Replace Nuclear force by classical gravity

43 Gluon dynamics Geometry. Confinement or deconfinement depends on geometry. Flavor dynamics by classical fields in warped geometry.

44 Result arxiv: to appear in JHEP by Y.Kim, Y.Seo, I. Shin, SJS stiffness

45 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. 45

46 Experiment stiff 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.

47 Pauli principle in hqcd. DBI action[q1,q2]=f(q)+s2(q1-q2)^2+ Positivity of S2 is equivalent to the Pauli principle in hqcd Parallel to 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.

48 Why analytic expression for symmetry energy. For the flat embedding approximation. Have confidence on

49 Dispersion relation for non-fermi-liquid E sym ρ 2/3 comes from E = p 2 E sym ρ 1/3 from E = p E sym ρ 1/2 E = p 3/2

50 Why interesting? The anomaly in 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.

51 Non-fermi Liquid in Nuclear system? G R (ω, k) = if ν kf < 1 2, ω (k) k z, z = 1 > 1 2ν kf h 1 k 1 v F ω h 2 ω 2ν k F Liu et. al If we choose ν kf = 1 3, we get E = p 3/2 E sym = ρ 1/2

52 Conclusion String theory is useful as well as interesting. Symmetry Energy can be calculated using the holographic principle. Physics of fermi surface for strongly interacting system will be Interesting issue. It can make the KoRIA more interesting project.

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