Bottom-up AdS/QCD through a few examples Y. Kim (KIAS)
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Transcript of Bottom-up AdS/QCD through a few examples Y. Kim (KIAS)
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Bottom-up AdS/QCD through a few examples
Y. Kim (KIAS)
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Contents
• Hard-wall model.• Examples: vector-vector correlator, vector-
meson mass, chiral condensate, Deconfinement temperature in AdS/QCD.
• Dense matter• Summary
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AdS/CFT Dictionary
• 4D CFT (QCD) --- 5D AdS• 4D generating functional --- 5D (classical) effectiv
e action• Operator --- 5D bulk field• [Operator] --- 5D mass• Current conservation --- gauge symmetry• Large Q --- small z• Confinement --- Compactified z• Resonances --- Kaluza-Klein states
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Let’s start from 2-flavor QCD at low energy aLet’s start from 2-flavor QCD at low energy andnd
attempts to guess its 5D holographic dual,attempts to guess its 5D holographic dual, AdS/CFT dictionaries.AdS/CFT dictionaries.
Bottom-up AdS/QCD model( look at QCD first !!! )
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5D field contents
Operator 5D bulk field
[Operator] 5D mass
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SU(2)LXSU(2)R gauge symmetry in AdS5
Current conservation gauge symmetry
5D Symmetry
Background: AdS5
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Confinement
Confinement IR cutoff in 5th direction
Polchinski & Strassler ‘00
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Hard wall model
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Example: vector-vector correlator
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Example: 4D vector meson mass
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Example: Chiral condensate
Klebanov and Witten ‘99
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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
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1. thermal AdS:
2. AdS black hole:
Transition between two backgrounds (De)confinement transition
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1. Cut-off thermal AdS:
2. Cut-off AdS black hole:
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z0
z=0
zh
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Hawking-Page at finite densityYK, B.-H. Lee, S. Nam, C. Park, S.-J. Sin, hep-ph/07062525, to appear in PRD.
For example,
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Fodor and Katz ‘01
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Nuclear matter in AdS/QCD YK, C.-H. Lee, H-U. Yee, hep-ph/07072637
Hard wall model with baryons:
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Mean field approach:
1. Chiral condensate
2. In-medium nucleon mass (iteratively)
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We may have to consider back-reaction of matters on the background.
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More phenominological approach
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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.