1. 1 Dynamical Holographic QCD Model Mei HUANG Institute of High Energy Physics, CAS Theoretical Physics Center for Science Facilities, CAS Seminar at USTC, Oct.10, 2013

2. 2 I. Why hQCD ? From UV to IR II. Pure gluon system: Quenched dynamical hQCD Glueball spectra III. Two flavor system: Dynamical hQCD Meson spectra Decay constant and form factor IV. Phase transitions V. Conclusion and discussion Danning Li, Mei Huang, arXiv:1303.6929 Systematic framework for chiral symmetry breaking & confinement

3. 3 I.Why hQCD ? From UV to IR

4. 4 QCD UV (Weak coupling): Asymptotic freedom Asymptotically conformal IR (Strong coupling): Chiral symmetry breaking & Confinement

5. 5 Strong QCD Quarks & Gluons (UV) QM, NJL, SM, HLS, CHPT, NRQCD …… DSE color flux tube Dual superconductor … Holographic QCD (hQCD) Effective field theories and models Lattice QCD Vacuum(IR)

6. 6 Quantum Gravity Strongly Coupled Gauge Theory Holographic Duality: Gravity/QFT General Gravity/QFT: AdS/CFT : Original discovery of duality Supersymmetry and conformality are required for AdS/CFT. In general, supersymmetry and conformality are not necessary

7. 7 Holographic Duality: (d+1)-Gravity/ (d)-QFT Holography & Emergent critical phenomena: When system is strongly coupled, new weakly-coupled degrees of freedom dynamically emerge. The emergent fields live in a dynamical spacetime with an extra spatial dimension. The extra dimension plays the role of energy scale in QFT, with motion along the extra dimension representing a change of scale, or renormalization group (RG) flow. arXiv:1205.5180

8. 8 Holographic Duality & RG flow Coarse graining spins on a lattice: Kadanoff and Wilson arXiv:1205.5180 J(x): coupling constant or source for the operator

9. 9 Holographic Duality & RG flow QFT on lattice equivalent to RG problem from Gravity RG scale -> an extra spatial dimension Coupling constant -> dynamical filed arXiv:1205.5180

10. 10 Holographic Duality: Dictionary Boundary QFT Bulk Gravity Local operator Bulk field Strongly coupled Semi-classical

11. 11 holographic QCD (5D) Real QCD world: Rich experimental data and lattice data 3rd step: gravity dual systematic framework 2nd step: deformed AdS 5 intelligent guess 1st step: just AdS 5 naïve try Build the connection between QCD dynamics and geometry Holographic QCD or gravity dual of QCD String theorists’ business: whether it can be deduced from 10D string theory ?

12. 12 QCD nonconformal N=4 Super YM conformal AdS 5 deformed AdS 5 Dilaton field breaks conformal symmetry A systematic framework: Graviton-dilaton system Input: QCD dynamics at IR Solve: Metric structure, dilaton potential

13. 13 Dynamical hQCD & RG A AdS 5 deformed AdS 5 QCD Dynamics at IR

14. 14 II.Pure gluon system: quenched dynamical hQCD

15. 15 5D action: graviton-dilaton Pure gluon system: Gluon condensate at IR: dual to

16. 16 Graviton-dilaton system A AdS 5 deformed AdS 5

17. 17 Glueball spectra:

18. 18 5D action for scalar glueball: scalar glueball:dual to

19. 19 1) Dimension-4 dilaton field No linear Regge behavior

20. 20 2) Soft-wall model with AdS 5 metric (“KKSS”) Cannot accommodate the ground state and the linear slope!

21. 21 3) Selfconsistent dimension-2 dilaton field Surprise! No extra parameter! deformed metric

22. 22 4) Dilaton field: quartic at UV and quadratic at IR However, the dual gluon operator of dimension-2 dilaton field is not known! Gauge invariant & Local operator

23. 23 Not sensitive to quartic form at UV. Determined by quadratic form at IR.

24. 24 Linear confinement Confinement potential QQ

25. 25 1, AdS 5 only gives Coulomb potential ! 2, Deformed metric structure is needed to produce the linear potential! Holographic dictionary: Metric structure determines the quark potential !

26. 26 Criteria for linear potential

27. 27 III. Two flavor system: Dynamical hQCD & Meson spectra Add flavor dynamics on gluodynamic background

28. 28 Deformed AdS 5 models for hadron spectra: hard-wall AdS 5 model soft-wall AdS 5 model: quadratic dilaton model 1, Hard-wall AdS 5 model: 5D hadron action AdS 5 metric

29. 29 Lowest excitations: 80-90% agreement However, no Regge behavior in the hard-wall AdS 5 model !

30. 30 A dilaton field to restore Regge behavior 2, Soft-wall AdS5 model or KKSS model However: only Coulomb potential, no linear quark potential AdS 5 metric

31. 31 Degeneration of chiral partners in KKSS model

32. 32 3, Modify action by a quartic interaction T. Gherghetta, J. I. Kapusta and T. M. Kelley, Phys.Rev. D 79 (2009) 076003; T. M. Kelley, S. P. Bartz and J. I. Kapusta, Phys. Rev. D 83 (2011) 016002; Negative mass square for scalar meson: instability

33. 33 4, Modify metric Yanqin Sui, Yueliang Wu,Yibo Yang, Zhifeng Xie, arXiv:0909.3887, PRD2010; Yanqin Sui, Yueliang Wu,Yibo Yang, arXiv:1012.3518, PRD2011 ……

34. 34 How to realize chiral symmetry breaking, & linear Regge behavior & linear quark potential in a unified model?

35. 35 Graviton-dilaton-scalar coupling system Action for pure gluon system: Graviton-dilaton coupling Action for light hadrons: KKSS model Total action: D.N. Li, M.H., arXiv:1303.6929

36. 36 Background with gluon condensate and quark-antiquark condensate

37. 37 Graviton-dilaton-scalar system A AdS 5 deformed AdS 5

38. 38

39. 39 IR asymptotic form constrained by linear potential: UV asymptotic form:

40. 40 Chiral fieldDilaton field

41. 41 Produced hadron spectra compared with data

42. 42 Produced hadron spectra compared with data

43. 43 Regge behavior and linear quark potential Linear confinement String model & confinement q q Flux tubes of color field = glue QCD and string theory I:

44. 44 Solved Metric Produced quark potential compared with Cornell potential

45. 45 Decay Constant and Form Factor

46. 46

47. 47 Smaller chiral condensate, smaller pion decay constant, better pion form factor

48. 48 large chiral condensate, better pion decay constant, worse pion form factor

49. 49 HQCD for Phase transitions

50. 50 5D graviton action: Metric structure, blackhole, Dilaton field and Dilaton potential should be solved self- consistently from the Einstein equations. Color electric deconfinement phase transition

51. 51 Experiences in constructing holographic QCD model tells us that: a quadratic correction in the deformed warp factor is responsible for the linear confinement. D.N, Li, S. He, M. H., Q. S. Yan, arXiv:1103.5389, JHEP2011

52. 52 Indeed, the positive quadratic correction dAdS5 model can fit all the finite temperature lattice QCD data for pure gauge SU(3) theory. D.N. Li, S. He, M.H., Q. S. Yan, arXiv:1103.5389, JHEP2011

53. 53 D.N. Li, S. He, M.H., Q. S. Yan, arXiv:1103.5389, JHEP2011

54. 54 D.N. Li, S. He, M.H., Q. S. Yan, arXiv:1103.5389, JHEP2011

55. 55 Trace anomaly D.N. Li, S. He, M.H., Q. S. Yan, arXiv:1103.5389, JHEP2011

56. 56 Heavy quark potential Electric screening Polyakov loop: color electric deconfinement D.N. Li, S. He, M.H., Q. S. Yan, arXiv:1103.5389, JHEP2011

57. 57 spatial Wilson loop spatial string tension Magnetic screening and magnetic confinement D.N. Li, S. He, M.H., Q. S. Yan, arXiv:1103.5389, JHEP2011

58. 58 V. Conclusion and discussion

59. 59 1, A systematic framework connecting QCD dynamics and geometry: graviton-dilaton for pure gluon system graviton-dilaton-scalar for hadron spectra 2, The linear Regge behavior as well as linear quark potential can be produced in a dynamical holographic model! The dimension-2 dilaton field at IR induces the linear confinement.

60. 60 3. We have realized chiral symmetry breaking, & linear Regge behavior & linear quark potential in a unified model!

61. 61 4. Dynamical hQCD & RG A AdS 5 deformed AdS 5

62. 62 Outlook

63. 63 Strong QCD Quarks & Gluons (UV) QM, NJL, SM, HLS, CHPT, NRQCD …… DSE color flux tube Dual superconductor … Holographic QCD (hQCD) Effective field theories and models Lattice QCD Vacuum(IR)

64. 64 Light flavor Hadron spectra Ground states: Effective models Excitation states: hQCD models Easy Hard Easy Heavy flavor Hadron spectra?

65. 65 Phase structure Chiral restoration Effective models Deconfinement hQCD models Easy Not easy Easy Hard

66. 66

67. 67 Hard for Effective QCD

68. 68 Easy for hQCD But we need a hQCD close to QCD! Dynamical hQCD model is one of the candidates!

69. 69 Thanks for your attention!