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Bottom-up AdS/QCD through a few examples

Bottom-up AdS/QCD through a few examples. Y. Kim (KIAS). Contents. Hard-wall model. Examples: vector-vector correlator, vector-meson mass, chiral condensate, Deconfinement temperature in AdS/QCD. Dense matter Summary. AdS/CFT Dictionary. 4D CFT (QCD) --- 5D AdS

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Bottom-up AdS/QCD through a few examples

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  1. Bottom-up AdS/QCD through a few examples Y. Kim (KIAS)

  2. Contents • Hard-wall model. • Examples: vector-vector correlator, vector-meson mass, chiral condensate, Deconfinement temperature in AdS/QCD. • Dense matter • Summary

  3. AdS/CFT Dictionary • 4D CFT (QCD) --- 5D AdS • 4D generating functional --- 5D (classical) effective action • Operator --- 5D bulk field • [Operator] --- 5D mass • Current conservation --- gauge symmetry • Large Q --- small z • Confinement --- Compactified z • Resonances --- Kaluza-Klein states

  4. Bottom-up AdS/QCD model ( look at QCD first !!! ) Let’s start from 2-flavor QCD at low energy and attempts to guess its 5D holographic dual, AdS/CFT dictionaries.

  5. 5D field contents Operator  5D bulk field [Operator]  5D mass

  6. 5D Symmetry Current conservation  gauge symmetry SU(2)LXSU(2)R gauge symmetry in AdS5 Background: AdS5

  7. Confinement Polchinski & Strassler ‘00 Confinement  IR cutoff in 5th direction

  8. Hard wall model

  9. Example: vector-vector correlator

  10. Example: 4D vector meson mass

  11. Example: Chiral condensate Klebanov and Witten ‘99

  12. Example: Deconfinement tempreature:Hawking-Page in a cut-off AdS5 E. Witten, Adv. Theor. Math. Phys. 2, 505 (1998), C. P. Herzog, Phys. Rev. Lett.98, 091601 (2007) So, gravitational action:~Nc2 Meson action:~Nc

  13. 1. thermal AdS: 2. AdS black hole: (De)confinement transition Transition between two backgrounds

  14. 1. Cut-off thermal AdS: 2. Cut-off AdS black hole:

  15. zh z0 z=0

  16. Hawking-Page at finite densityYK, B.-H. Lee, S. Nam, C. Park, S.-J. Sin, hep-ph/07062525, to appear in PRD. For example,

  17. Fodor and Katz ‘01

  18. Nuclear matter in AdS/QCD YK, C.-H. Lee, H-U. Yee, hep-ph/07072637 Hard wall model with baryons:

  19. Mean field approach: 1. Chiral condensate 2. In-medium nucleon mass (iteratively)

  20. We may have to consider back-reaction of matters on the background.

  21. More phenominological approach

  22. Summary • Although there is no robust proof, bottom-up AdS/QCD approaches are describing QCD relatively well. • It is important to see what we can do, what we cannot do and what we should not do with the approach.

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