1. Summary WG4
Elisabetta Pallante
EF07 Orsay

2. Analytic methods for non perturbative QCD

3. What about AdS/CFT ? Resonances and ghosts Bounds from unitarity
crossing analyticity
plenary

6. From AdS/CFT to AdS/QCD ?
Quark Gluon Plasma at RHIC: confinement and running
coupling of secondary importance
Up – down approach
Bottom – up approach
Hadron physics ?
‘t Hooft coupling l=g2Nc
not smooth ?
Shuryak hep-ph/

7. Scalar Mn2 = 4n + 8 Vector Mn2 = 4n + 12 r meson Mn2 = 4n + 4
spectrum given by 1d Schroedinger equation
Play with modifications of dilaton background and/or bulk geometry

8. Resonances

9. Large-NC resonance relations from partial wave analyses
EuroFlavours 07, November 2007
Univ. Paris-Sud XI - Orsay
Large-NC resonance relations from partial wave analyses
J.J. Sanz-Cillero (IFAE - UAB)
Z.H. Guo, J.J. Sanz-Cillero and H.Q. Zheng [ JHEP 0706 (2007) 030 ]; arXiv:  [hep-ph]

10. Study Partial-Wave scattering amplitudes in the s,t,u channels
through once-subtracted dispersive relations at large-Nc
 (good high energy behaviour)
Matching with cPT up to order p6
LECs
MR , GR
Prediction of LECs at order p6 of the chiral lagrangian

11. New dispersive method for the the study
of LECs and resonance constraints at large-NC
Easy implementation of high & low-energy constraints
independent of the realization of the resonance lagrangian
Successfully checked for a wide set of different
phenomenological lagrangians
Useful tool for future studies of other scattering amplitudes

12. Ghosts ?

14. Spin 1 massive fields: Proca equation and all that …
Project onto physical d.o.f. :  kinetic t.
Nothing more than that …
Higher spin Rarita-Schwinger fields
More intricate: acausal propagators
Shamaly, Capri Unified theories for massive spin 1 fields, Can.J.Phys.
51 (1973)1467, Annals of Phys. 74 (1972)503

15. Analitycity Unitarity
Crossing

18. Possibly related to radius
of convergence …

20. Analitycity Unitarity Crossing
A few more references on axiomatic principles
Ananthanarayan, Toublan, Wanders, PRD 51 (1995) 1093
Pham, Truong, PRD 31 (1985) 3027 higher derivatives
Dita, PRD 59 (1999) positivity constraints
Lang, Porod, PRD 21 (1980) pK phase shifts
Lang, Stefansen, PLB 79 (1978) 479

21. Future In the last two decades we have reshaped our view of
quantum field theories. EFT are at the foundations of modern
quantum field theory.
Effective field theories of low energy QCD significantly
contributed to our modern view
Where is the future of EFT?
Bridging (SU)GRA
theories and
4-dimensional universe
High precision very
low energy physics
e.g. EDM
New formalisms?
Charm decays
Intermediate T,m