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.