Quantum Matter Classical Spacetime

Transcription

1 Quantum Matter with Classical Spacetime Sang-Jin Sin (Hanyang Univ.

2 Introduction One way to look: history of physics is that of simplification & unification. Simplify things to the end, until one reach the fundamentally basic object. Until it is calculable. Idea of atom. Reductionism. Unification: view different things as the same thing. 2

3 Example 1: Relativity In 1604, Galileo found that constantly moving frame is the same as the stationary frame. (to explain 1.why earth can move. Aristotle said: force is needed to keep motion. 2. why table does not leave the earth.) 1st law of mechanics. 1 st Revol. of physics from 2000 years of Aristotle regime. v is nothing, v is first non-trivial thing and is prop to force. In 1905: Einstein said Space~Time, Mass ~ Energy In 1910, Einstein claimed gravity ~ accelleration ~ frame change : not a force. Then curved trajectory should be due to the curved geometry. Why curved? Due to energy/momentum. GR. 3

4 Example 2, Force unification. 1820, Orsted found Magnetism and electricity are related. Faraday and finally Maxwell realized that E and M are just different aspect of the same object. First and most famous example of unification. Similar unification was repeated in 20 century. 4 forces: E&M, weak, strong, gravity. In 1967: Weinberg found : E&M=weak Einstein wanted to unify E&M and gravity but FAILED. String theory want to unify all of these forces. And so far it is the only candidate to unify all of them 4

5 Example 3. Quantum mechanics Quantum mechanics is about duality of wave and particle. Any fundamental object in nature has both particle and wave nature. That is, Particle ~ Wave. The so called classical behavior of baseball is an Emergent behavior due to the collective motion: Each electrons and protons has duality but they show ONLY particle nature if they move coherently (as a baseball). Similarly, Photons show ONLY wave nature when they move/act collectively. In each case the classicality is associated with the large number. It is an Emergent phenomena. 5

6 Ex 4. Matter and space-time. Spin 1 theory of interaction between fundamental matter, which is always of quantum nature. Spin 2 variation of space-time These two LOOKS completely different! Today s message of talk is : they are different ends of the same object, schematically Matter = Spacetime This scenario was constructed by the string theory And it is today s theme. 6

7 Modern view of atom 7

8 Our focus 8

9 History In 1930: photon, e, p, n, mu, pi and neutrino, people were happy: all the elementrary building blocks and glues are all found. In 1960: tens of resonances living only 10^ {-24} sec. strongly interacting. Order of magnitude stronger than E&M. Physics lost simplicity Gellmann classified them using quarks and restored simplicity. 9

10 however Field theory is useless for strong interaction. FT=th of particle int. based on free particle and their interaction. Calculation is done by perturbation: X = c 0 + c 1 g + c 2 g 2 + c 3 g if g>1, we can not calculate anything. If first order is not enough, calculating higher order is meaningless. Need new frame. S-matrix: analyticity, crossing symmetry, Boostrap. (1943: Heisenberg. n,p mag.mnt: extended obj. ) 10

11 progress: Regge trajectory. 11 Infinite # particle=extended nature of object.

12 Birth of string theory Particle field theory obviously can not give such infinite spectrum. Veneziano found an empirical formula for 2-2 scattering formula satisfying the S-matrix axioms as well as Regge trajectory. Beta function in s,t. Nambu, Nielson, Susskind 1970 found that Veneziano formula is obtained from the spectrum of string. In brief string theory can give Regge Trajectory. In low energy, n.p have size and it can be described as 1-dim. Object. Not 3d. 12

13 up and down of string theory Deep inelastic scattering experiment. e-p. quarks inside proton is free to move and point like. QFT revived. pqcd explained why this happens by asymptotic freedom while string theory could not. [Npage] 13

14 What QCD is about? Interaction between the quarks 14

15 QCD and other forces 15

16 QCD in high energy. Weakly interacting (AF) Nobel prz 16

17 QCD in low E: strongly int. And Unsolved. Weak v.s Strong int. For strong int. Not clear even what is particle

18 up and down of string theory *1974 Scwartz-Sherk: graviton in closed string theory. String theory as gravity theory. But string scale: 1GeV 10^{19} GeV. *1984: string theory is OK with quantum mechanics Theory of everything. [Nnpage] 18

19 What is big deal about Gravity QM is a fundamental principle on the nature of matter. Relativity is about symmetry of space time. Special relativity + QM anti-particle. General relativity +QM Trouble 19

20 QM gravity Every other force: Force = - gradient of (pot. Energy) Gravity: curvature = G (energy itself) w/o derivative! QM fluctuation infinite vac. energy. infinite curvature 20

21 Origin of vac. Energy Uncertainty principle p x + + In Point like theory, arbitrary vac. energy is possible by (Delta x 0) 21

22 Why String theory is finite? Finite theory for quantum gravity. Idea: stringy uncertainty principle: presence of minimum length disappearance of UV divergence 22

23 Up and down of string theory However, But too many theory. Compactification! Too many vac. 1995: Duality in string theory. 5 possible string theories are different limit of the same M theory. 1996: Polchinski found D-brane. 1997: Maldacena found AdS/CFT birth of holographic physics. 23

24 So much for string History. back to our theme: strong interacting low e QCD General idea: Reformulate theory in terms of new degree of freedom whose interactions are weak. Duality

25 String theory idea replace strong force by classical geometry this is called AdS/CFT What is it?

26 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: 26

27 p-dim Membrane D-brane and AdS/CFT Whose vibration is by that of open string ending on it. The low energy physics: SU(N) SYM Stack of D-brane space time warp near D: AdS static source(d) static geometry. 27

28 AdS/CFT Now consider vibration of D brane in 2 views. 1. motion of source ~ open string by def. 2. motion of the field ~ closed string in curved geometry. This source-field equivalence is called ads/cft. Analogy: D-brane = electron. AdS=Coulomb field Open string: dipole motion of electron. Closed string: radiation field. AdS/CFT=electron motion can be traced by looking its radiation field. 28

29 Summary String in AdS5 is dual to SYM in 4d. 5d v.s 4d Holographic corresp. For large coupling, closed string can be replaced by gravity AdS/CFT gravity/gauge dualtiy 29

30 Shape of AdS Eschers s Angels and devils" 30

31 Consequence of duality 1. Gluon dynamics is replaced by ads gravity. 2. For large N_c, gravity is weakly coupled. 3. Correlation function in 4d can be calculated by the classical dynamics at the 5d AdS. holographic.

32 Thermalized system ~ BH in ads

33 System with dense matter Conserved number local charge electric potential pot.

34 Meaning of extra dimension Einstein eq. encodes flow. AdS d+1 d!1,1 R Minkowski BOUNDARY... IR r UV IR r UV Figure 1. The left figure indicates a series of block spin transformations labelled by a parameter r. The right figure is a cartoon of AdS space, which organizes the field theoryinformationinthesameway.inthis sense, the bulk picture is a hologram: excitations with different wavelengths get put in different places in the bulk image. Figure from by

35 Is string theory for real phyiscs? String theory is notorious not to be a physics. Origin: enterance of plank scale. Closed string has gravity. Resolution: 1. Lower Mp. With extra dim. Idea. 2. Cancel out or Hide Mp: In pure ads/cft, string scale cancel due to conformal inv. Break scale sym. hide in mass parameter. 35

36 Can St.Th. be verified in Lab? Yes, I think it is. Example: RHIC found it or its usefulness. 36

37 Relativistic Heavy Ion Collider (Brookhaven N.L) Au-Au collision E~200 GeV/nucleon Seek quark-gluon plasma(qgp) 09/05/12 korea univ. 37

38 RHIC Findings (my paper) Collective(Elliptic) flow: (th/ ) Perfect fluid : ( , ) Jet quenching (hep-th/ ) Early thermalization (hep-th/ ) all indicates sqgp

39 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 perfect fluid

40 Perfect fluid T µν = T µν 0 + ηt µν 1 Exp+hydro simulation η/s < 0.1 /k B While perturbative evaluation ~1/g^4lng ads/cft : η s = 4πk B Son+Starinets+Policastro (2002) Universal value, model independent; no other theory can explain it. The most known example of experimental evidence of string.

41 Jet-Quenching Energy Loss Problem.

42 Holography of radiation SJS with Zahed(hep-th/ , PLB) gluon propagation at boundary v.s null geodesic along the path passing the center. P Position of P r( )=Rtan We get point-sphere correspondence.

43 Holography of radiation in Black hole background P Maximal propagation distance= P will be absorbed into the BH or never get to it according to the observer. The dual picture to this is stopping at

44 Early thermalization (hep-th/ ) Thermalization in 3+1= BH formation in ads. why BH in 1 dynamical time? Ans: falling in AdS and time-focusing effect It enhences black hole formation in AdS compared with flat spacetime.

45 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 fct Transport Coeff. Ads/Cft can calculate <JJ>, <TT> easily. viscosity, conductivity, charge, susceptibility,

46 More theoretical use Strong int. perturbation does not work. Need to sum infinitely many diagram. Resummation technique by Dyson Schiwinger eq. This technique involve truncation to special class of diagram. (Ladder Type). For weak coupling this gives non-perturbative result. For strong coupling, DS is not justified. 46

47 Nevertheless people solve DS since there is not anything better. Some interesting result is obtained using this method. Question: Should we trust it? Proposal: Use ads/cft to calculate the same objects and see what happen. 47

48 Thermal mass and Plasmino. Two famous characters of massless fermion In hot Medium, One is Thermal mass ( Klimov 82, Weldon 83) the other is Plasmino (Braaten, Pisarski 89 ) p<<m f : ω ± (p) ± 1 3 p, p>>m f : ω ± (p) p. ω / m T Dispersion relation The plasmino mode has a minimum at finite p. 48

49 Problem these results are based on Hard Thermal Loop approximation which uses Dyson-Scwinger idea to resum the diagrams. So we can not trust its validity in sqgp Q: What string theory says about the thermal mass and plasmino. 49

50 Result : Dispersion relation for Confining case(t independent) There is Plasmino only for large but not too large chemical potential. µ 1 µ µ 2.. Extreme high density behavior is very complex and rich and will not be presented here.

51 III. String theory at KoRIA There is a National project called KoRIA. We spend $ 0.4 billion. Can we say something about it? 51

52 Result for deconfing case: 1. Vanishing thermal mass for zero density 2. No plasmino for zero density (a) (b)

53 KoR(are)I(sotope)A

54 Valley of stability: Pauli v.s Coulomb Density dependence of the valley position is important

55 Symmetry Energy Liquid Drop Model Bethe-Weizsäcker formula (1935): E B = a V A + a S A 2/3 Z(Z 1) (N Z) 2 + a C + a A 1/3 A A Coulomb Pauli δ(z, N) E(ρ, α) E(ρ, 0) + S 2 (ρ) α 2, α (N Z)/A. It determines the curvature of valley of Stability.

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

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

58 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.

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

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

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

62 Pauli principle in hqcd. Driving force of Z=N is Pauli principle Dual theory is classical theory, while PP is quantum. How to formulate PP in classical context. dual E-charge dual to baryon (neutron) number. There is a Coulomn repulsion. What is the dual to it? Answer: Coulomb repulsion of the dual E&M is dual of Pauli prepulsion.

63 System with dense matter 4d Neutron number 5d Electric charge

64 Conclusion Physics achieve its goal from simplification and unification. string theory can achieve unification as well as a dual picture which enables calculation which is otherwise impossible. It (or its usefulness) can be tested in Lab.