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3rd International Workshop On High Energy Physics In The LHC Era
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QCD : Theory of strong interactions Problem: strong coupling limit ( lattice, ….. ) Gravity ?Strings provide relationship History 1) Duality in strong interactions Dual resonance models Veneziano formula Derived from string model Contains Regge behavior QCD string
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2) Regge Behavior easily obtained from string meson model Planar diagrams dominate 3) Large Nc Relation between Feynman diagrams of gauge theory and two dimensional surfaces.
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AdS / CFT Where is the QCD string ? Classical Supergravity in AdS N=4 Super Yang-Mills at boundary Where does it come from ? Open – close string duality Holography
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Consequences : 1) Gauge – gravity duality. Massless open string modes Gauge fields Massless closed string modes Gravitons Tree level gravitational interactions Gauge interactions at one loop 2) Short – Long distance relationship Short r SU(N) gauge coupling weak (asym. freedom) Gravitational coupling strong (branes are massive) Long r Gravity weak Open string interaction strong
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Mathematical correspondence Generating functional of gauge theory Classical action Correlation functions in gauge theory Fields in the bulk Is there a holographic dual of QCD ? QCD at strong coupling weak coupling ?
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QCD Confines Chiral condensate Discrete spectrum Running coupling Has quarks Not Supersymmetric Nc = 3 Not confining No chiral condensate Continous spectrum Conformal Adjoint matter Supersymmetric Nc large N = 4 SYM
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Approaches : 1) Top – down Brane construction in string theory, which at low energies describes a gauge theory with QCD features. 2) Bottom - up Specify extra-dimensional space time geometry and the fields that propagate, based on QCD properties. Example: SU(2) x SU(2) gauge symmetry of QCD Approximate chiral symmetry of QCD Add scalars, which can give spontaneous symmetry breaking to isospin
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Confinement, … T(Hawking) of BH related to T(gauge theory) Soft wall: background scalar field
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Finite temperature Not confining Not supersymmetric Not conformal Dbye screening Strongly-coupled plasma of gluons and fundamental matter Not confining Not supersymmetric Not conformal Dbye screening Strongly coupled plasma of gluons and adjoint and fundamental matter. QCD N = 4 SYM Very similar !! T > Tc
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Holographic hydrodynamics Perfect fluid at rest Static 5d black hole in the bulk Fefferman – Graham coordinate system Perfect fluid (AdS / CFT dictionary)
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Black hole vs Perfect fluid Black hole
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Beyond static configuration Dual relations to Bjorken flow Boost invariant expansion of the QGP Coordinate system General family of solutions
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Perfect fluid Black hole moving in fifth dimension Late time dynamics Bjorken flow
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Beyond perfect fluid derive viscosity (Kubo formula) Graviton- BHole absorption CS Early time dynamics ? Landau flow ?
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Conclusions 1)AdS/CFT : Incredible number of applications. 1)Still a lot of things to do: corrections, …. Meson wave function from holographic models. A. Vega, I. Schmidt, T. Branz, T. Gutsche, V. E. Lyubovitskij, Phys. Rev. D80: 055014,2009.A. Vega,, T. Branz, T. Gutsche, Phys. Rev. D80: 055014,2009. Hadrons in AdS/QCD correspondence. A. Vega, I. Schmidt, Phys. Rev. D79: 055003, 2009.A. Vega, I. Schmidt, Phys. Rev. D79: 055003, 2009. Glauber-Gribov approach for DIS on nuclei in N=4 SYM. E. Levin, J. Miller, B.Z. Kopeliovich, I. Schmidt, JHEP 0902: 048, 2009.E. Levin, B.Z. Kopeliovich, I. Schmidt, JHEP 0902: 048, 2009. Scalar hadrons in AdS(5) x S**5. A. Vega, I. Schmidt, Phys. Rev. D78: 017703, 2008.A. Vega, I. Schmidt, Phys. Rev. D78: 017703, 2008.
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