1 / 28

High Energies Scattering in the AdS dual to “QCD”

High Energies Scattering in the AdS dual to “QCD”. Richard C. Brower Boston University. Lattice 2007 --- August 3. Progress since Lattice 2006: “The Pomeron and Gauge/String Duality” by Brower, Polchinski,Strassler & Tan (BPST) hep-th 0603115. (very) Few Related References. Flat space:

adli
Download Presentation

High Energies Scattering in the AdS dual to “QCD”

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. High Energies Scattering in the AdS dual to “QCD” Richard C. Brower Boston University Lattice 2007 --- August 3 Progress since Lattice 2006: “The Pomeron and Gauge/String Duality” by Brower, Polchinski,Strassler & Tan (BPST) hep-th 0603115

  2. (very) Few Related References Flat space: ‘tHooft, “Graviton Dominance in Ultra-High-Energy Scattering” PL B198 (1987). Amati, Ciafaloni & Veneziano “Superstring Collisions at Plankian Energies”, PL B 197 (1987). Bo Sundborg, “High-Energy Asymptotics: The one-loop string amplitude and resummation” NP B306 (1988) AdS5: D’Hoker, Freedman, Mathur, Matusis & Rastelli, “Graviton exchange and complete 4-point functions in the AdS/CFT correspondence” hep-th/9903196 v1 Cornalba, Costa, Penedones & Schiappa, “Eikonal Approximation in AdS/CFT: From Shock Waves to Four-Point Functions” hep-th/0611122 v1 Alday & Maldacena “Gluon scattering amplitudes at Strong coupling” hep-th/0705.0303 v1

  3. Outline • Motivation • Dual 5-d Geometry of High Energy scattering • BFKL vs BPST Pomeron: ( log2(s) »¸ = g2YM Nc ) • Eikonal for AdS5 Gravity: ( ¸ >> log2 s ) • Eikonalization + confinement ) Froissart Bound

  4. Phenomenological Motivation Diffraction production will dominate LHC events. Diffraction is a leading contender for the discovery of the Higgs! What is its rate? % of non-diffractive events fall like 1/Etot LHC Diffractive Higgs: Forward Proton 420m Exp. Of course Jets are often cleaner and Diffraction is still badly understood.

  5. “Diffractive and Total Cross Section at Tevatron and LHC” (K. Goulianos hep-ex/0707.1055v1)

  6. Theoretical Motivation QCD obeys the (non-perturbative) Froissart theorem: • ¾Tot(p+p ) X) = m-2p C(m¼/mp) log2(s/s0) + L Questions: Is C(m¼/mp) >0 ? What is its value? What are the events that give C > 0? Does the AdS/CFT provide a generic mechanism C>0? Can one in principle compute C(m¼/mp) on then “lattice”?

  7. p2 p3 s = (p1 + p3)2 p4 p1 t = (p1 + p2)2 Optical Theorem: High Energy Elastic Scattering Regge:

  8. Definition: Nc!1 contributions The Pomeron ´ the vacuum exchange contribution to scattering at high energies at leading order in 1/Nc expansion. where ¸ = g2Nc & gs = 1/Nc

  9. k’2 k2 k1 k’1 ln s t = - (k1 + k2)2 BFKL: Balitsky & Lipatov; Fadin,Kuraev,Lipatov‘75 ¸ = g2 Nc' 0 • Sum diagrams 1st order in g2 Nc and all orders (g2 Nc logs)n gives cut starting at j0 = 1 + ¸ ln 2 /¼2. • Accidentally “planar” diagrams (e.g. Nc = 1) and conformal. • BKFL equation for 2 “reggized” gluon ladder is L = 2 SL(2,C) spin chain to one loop order . • BFKL is NOT a REGGE POLE! DIFFUSION “off shell k2 > 0” GLUON “virtuality”

  10. Moebius (aka SL(2,C)) invariance 1 L 2 3 2-body Casimirs

  11. AdS5/CFT Dictionary The 5th dimension is conformal dilations

  12. b2 °*(Q2) b? “Five” kinematical co-ordinate is size z / z’ of projectile/target b1 5 kinematical Parameters: 2-d Longitudinal p§ = p0§ p3' exp[ § log(s/¤qcd)] 2-d Transverse space: x’?- x? = b? 1-d Resolution: z = 1/Q (or z’ = 1/Q’)

  13. Boosting AdS5 to AdS3 isometries O(4,2) isometries with z = R2/r DIS : SLR(2,R)x SLL(2,R) BFKL: SL(2,C)

  14. High energy Graviton exchange Kernel is AdS3 Green’s function Strong Pomeron kernel: same structure in J-plane!

  15. N = 4 SYM Leading Twist ¢(j) vs J=j • = 0 DGLAP (DIS moments) (0,2) T = 0, BFKL j = j0 @ min 

  16. + + + Eikonal Expansion Born term “sum” to get

  17. Two approaches to Eikonal Approximation sum of leading large s contribution for perturbative series. propagation in a shock wave gravitational background of target. (‘tHooft’s method) Again in AdS5 space can do it both ways. We start with sources at the boundary and write down Witten (AdS5 Feynman) diagrams for the “S-matrix” with a “hardwall” IR regulator.

  18. Witten Diagram Summation

  19. AdS5 Eikonal Sum Note: 3-d “impact” space or Matrix eikonal We calculated explicitly the the box diagrams to see beginning of series expansion in \chi. The kinematics is basically the same as in Cheng-Wu’s classical paper from 1968.

  20. Shock Wave Eikonal Formulation 1.Solve linearized Einstein equ: 2.Propagate across shock: p+1 p-2

  21. IR cut-off or Confining Hard Wall Model(quick and dirty example of confining duals) Large Sizes Add Confinement IR wall! String/Glueball

  22. Broken scale invariance in the 5th dimension (r) Hadron/Glueball Massive Onium Current r -4 r- IR WALL r- r !1 r = rmin

  23. Kernel for hardwall at z =1 Khw/Kconf b? z (z’ = 0.01)

  24. Born Term for Hard Wall model z=w z=w x? x? Kconf(z,z,x?) - Khw(z,z,x?) Khw(z,z,x?)/Kconf(z,z,x?) B.C.

  25. Theory Parameters: Nc & ¸ = g2 Nc log(s) Weak BFKL Black Hole Eikonal Expansion AdS BFKL AdS Gravity log(b) Confining Conformal

  26. Concluding remarks • The KK modes represents a matrix version of eikonal formula like super string scattering of Amati, Ciafaloni and Veneziano ( “string bits are frozen” ). • Unitarization: Hardwall (confining) eikonal sum (probably) saturates the Froissart --- work in progress. (Brower, Strassler and Tan) • More central collisions require non-perturbative --- triple Regge, fan diagrams, black hole or plasma ball deconfinement region etc. See color glass condensate phase?

  27. N = 4 SYM ´ AdS5 x S5Open stings are Gluons dual to closed string Gravity. Dynamics of N D3 branes at low energies is (Super) SU(N) YM. Their mass curves the space (near horizon) into AdS5 and emits closed string (graviton) gmn gravitons Am gluons D3-branes

  28. see “Total cross section at Tevatron and LHC” K. Goulianos hep ex/0707.1055v1

More Related