3rd International Workshop On High Energy Physics In The LHC Era.
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Some ideas about CFT/AdS 3rd International Workshop On High Energy Physics In The LHC Era
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Transcript of 3rd International Workshop On High Energy Physics In The LHC Era.
Some ideas about CFT/AdS
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
History1) Duality in strong interactions
Dual resonance models
Veneziano formula Derived from string modelContains 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 relationshipShort
rSU(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
ConfinesChiral condensateDiscrete spectrumRunning couplingHas quarksNot
SupersymmetricNc = 3
Not confiningNo chiral
condensateContinous
spectrumConformal Adjoint matterSupersymmetricNc 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
supersymmetricNot conformalDbye screeningStrongly-coupled
plasma of gluons and fundamental matter
Not confiningNot
supersymmetricNot conformalDbye screeningStrongly 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.
2)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.
Hadrons in AdS/QCD correspondence. 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. Scalar hadrons in AdS(5) x S**5. A. Vega, I. Schmidt, Phys. Rev. D78: 017703, 2008.
