3rd International Workshop On High Energy Physics In The LHC Era

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

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.

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

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

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 ?

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

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

Confinement, … T(Hawking) of BH related to T(gauge theory) Soft wall: background scalar field

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

Holographic hydrodynamics Perfect fluid at rest Static 5d black hole in the bulk Fefferman – Graham coordinate system Perfect fluid (AdS / CFT dictionary)

Black hole vs Perfect fluid Black hole

Beyond static configuration Dual relations to Bjorken flow Boost invariant expansion of the QGP Coordinate system General family of solutions

Perfect fluid Black hole moving in fifth dimension Late time dynamics Bjorken flow

Beyond perfect fluid derive viscosity (Kubo formula) Graviton- BHole absorption CS Early time dynamics ? Landau flow ?

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: ,2009.A. Vega,, T. Branz, T. Gutsche, Phys. Rev. D80: ,2009. Hadrons in AdS/QCD correspondence. A. Vega, I. Schmidt, Phys. Rev. D79: , 2009.A. Vega, I. Schmidt, Phys. Rev. D79: , 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, Scalar hadrons in AdS(5) x S**5. A. Vega, I. Schmidt, Phys. Rev. D78: , 2008.A. Vega, I. Schmidt, Phys. Rev. D78: , 2008.