1. New Perspective for QCD: String /Gauge Duality Evidence for QCD as an Effective String Theory Maldacena’s Counter Revolution: Gauge/Gravity Duality Re-discovery of QCD String and Extra Dimensions QCD in Strong Coupling: Hard vs Soft Pomeron in AdS Background Confronting String Theory with High Energy Scattering Small-x and Diffraction, FNAL, 2003----Chung-I Tan, Brown

2. I. Evidence for QCD as String Asymptotic Freedom Confinement Force at Long Distance-- Constant. Tension/Linear Potential, coupling increasing, Quarks and Gluons strongly bound “Stringy Behavior”

3. String Modes: Vibrational Modes and Rotational Modes

4. Tests for String Excitations Open String Mesons Closed String Glueballs String Junction Baryons Open String with Fixed Sources Can be tested using Lattice Gauge Theory: Discrete sites ---> Finite Variables Positive Euclidean Action ---> Numerical Simulation Phenomenological tests Moriond proceedings last 30 years

5. Wilson Loop as Surface Sum Searching for evidence of String!

6. Recent Results of Martin Luscher et al. String Excitation Energies can be measured by Wilson Loop Correlation function, Precision measurement ==> effective bosonic string. Further “structure” yet to be understood.

7. M. Luscher and P. Weisz, J. H. E. Physics, 07 (2002) 328 K. J. Junge, J. Kuti, C. Morningstar, hep-lat/0207004

8. Luscher’s Conclusion

9. II. String/Gauge Duality Early String Theories ==> Theory of Everything Maldacena ==> New Era for YM Theories

10. How Can QCD be a String Theory? Topological Expansion

11. “Failure” of Superstrings in Flat-Spacetime (1973~1998) Zero mass states: (gauge/graviton) Extra dimensions: D=4+6=10 Supersymmetries: No Hard Scattering:

12. AdS/CFT Duality (1998--) Strong-Weak Dual Example: Ising-model--(high-low temp.) 4d “Gauge” dual to “Geometry” in higher dim Absence of 4 dim-Graviton Wilson loop expectation ~ sum over surfaces in the bulk with loop in boundary 4d YM Theories at weak coupling is dual to higher dim String Theories with deformed AdS Background.

13. Maldacena’s String Counter Revolution Open String Closed String duality YM Wilson Loops Expectation Values in Bulk!

14. Minor Problem: Wilson Loop in AdS/CFT For rectangular loop: Extension into minimum surface in r-dir Surface into AdS space Zero Tension for QCD String---> Unacceptable

15. III. Re-discovering QCD String Witten’s proposal---AdS/BH metric Deformed AdS Space, Massive Graviton Soft Pomeron and Tensor Glueball QCD String Tension Breaking Supersymmetry

16. Witten Proposal

17. AdS/BH metric

18. Minimum Surface for Wilson Loop

19. M. Luscher and P. Weisz, J. H. E. Physics, 07 (2002) 328

20. VI. QCD in Strong Coupling and HE Scattering IR Physics--Glueballs as AdS Gravitons at strong coupling. UV Physics--Parton counting rules for wide-angle scattering. Stringy Deconfinement. Fat vs Thin Strings. Hagedorn Transition (aka deconfinement ?) Pomeron as Massive Graviton. BFKL Pomeron, Regge, DIS, Froissart Bound, ………..

21. QCD after Brane Revolution Effective degrees of freedom---massless fields of type IIA String theory Confinement by AdS/BH background New chapter for non-perturbative QCD Weak Coupling --> Perturbative QCD :unchanged Confinement --> Dual description in AdS : weak field approx.

22. Glueball Spectrum R. Brower, S. Mathur, and C-I Tan, hep-th/0003115, “Glueball Spectrum of QCD from AdS Supergravity Duality”.

23. Pomeron in Gauge/Gravity Duality Pomeron as Massive Graviton! Intercept “lowered” from 2! Interpolate with BFKL due to “hard” at AdS Bdry.

24. Physics at Different QCD Scales in AdS Space

25. Tensor Glueball/Graviton Wave functions n=1n=3 n=8Potential n=0 Randall-Sundram graviton r min r

26. QCD Rutherford Experiment At WIDE ANGLES QCD exhibits power law behavior: where n=  i n i is the number of ``partons'' in external lines. Actually QCD is only conformal up to small asymptotic freedom logs. The OPE gives in terms of the lowest twist  i.

27. Wide Angle Scattering The 2-to-m glueball scattering amplitude T(p 1,p 2, , p m+2 ) for plane wave glueball: This is a check on the underlining universality of Maldacena's duality conjecture. scatter via the string(M-theory) amplitude: A(p i, r i, X i ) in the 10-d (or 11-d) bulk space (x,r,Y): AdS 5 £ X with IR cut-off on r > r min or 10-d IIB string theory AdS 7 £ S 4 $ Black Hole with horizon r = r min or 11-d M-theory. We now discuss two different approaches to the QCD string that both give the correct parton scaling formula.

28. 10-d String theory Approach Due to the Red Shift in the Warped Co-ordinate,  s = (R/r)  x,a plane wave glueball, exp[i x p], scatters with a local proper momentum, String is UV shifted in the YM’s IR. (This is the so called UV/IR connection.) THUS wide angle scattering IS exponentially suppressed in the region r 2 [r min,r scatt ] HOWEVER there is a small remaining amplitude at large r that that gives the correct conformal scaling of the naive parton model! E.g for a scalar glueball  » r -4 corresponding to n i = 4 for the YM operator, Tr[F 2 ], in exact agreement with the parton result.

29. Summary on Hard Scattering (3) Compared with lowest order perturbative results: (1) AdS 5 Hard Scattering (Polchinski-Strassler): WHY is it same QCD perturbative result with g 2 N ! (g 2 N)^2? (2) AdS 7 Hard Scattering (Brower-Tan): WHY does this only depend on the string tension?

30. Soft vs Hard Regge Scattering Similar arguments can be applied to the Regge limit: s >> -t Dominant scattering at large r, gives a BFKL-like Pomeron with almost flat ``trajectory'' (actually a cut in the j-plane) The IR region, r ' r min, gives soft Regge pole with slope  ' qcd »  ' R 3 /r 3 min The ``shrinkage'' of the Regge peak is caused the soft stringy ``form factor'' in impact parameter:

31. V. Future Developments Improved Confining Background Challenges: BFKL, Froissart bound, Massless Quarks, Chiral Symmetry, …….. ………….. Beyond strong coupling or Strong Gravity. See you at next FNAL Small-x Meeting!