N=4 SYM in High Energy Collision and the Kalb-Ramond Odderon in AdS/CFT

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1 N=4 SYM in High Energy Collision and the Kalb-Ramond Odderon in AdS/CFT Chung-I Tan Brown University Dec. 19, 2008 Miami R. Brower, J. Polchinski, M. Strassler, and C-I Tan, The Pomeron and Gauge/String Duality, hep-th/ ; R. Brower, M. Strassler, and C-I Tan, hep-th/ , hep-th/ ; R. Brower, M. Djuric and C-I Tan, Kalb-Ramond Odderon and AdS/CFT, arxiv: (hep-th). Also: arxiv: (hep-ph).

2 Outline Physics at High Energy in near-forward scattering: Pomeron as metric fluctuations in AdS space: Graviton is a fixed Regge Cut in AdS: ( Conformal Invariance ) Pomeron as a Reggeized Massive Graviton: (Confinement ) Kalb-Ramond Field and Odderon: Aspects of Analyticity, Unitarity and Confinement: Saturation, Confinement, etc.

3 I. Diffractive Scattering at High Energies

4 Regge Behavior and Regge Trajectory A s J(t) = s α(0)+α t 4

5 Total Cross Sections A s J(t) = s α(0)+α t A σ total A(s, 0)/s S J(0) 1 s α(0) 1 α(0) > 1

6 High Energy Experiments Suggest Exchanging C=+1 color-singlet state with effective spin Exchanging C=-1color-singlet state with effective spin These can be calculated by perturbative technique 6 (Lipatov et al.)

7 Gauge/String Duality C=+1: Pomeron <===> Graviton C=-1: Odderon <===> Kalb-Ramond Field 7

8 II: Gauge/String Duality Pomeron as metric fluctuations in AdS Strong <==> Weak duality Scale Invariance: Confinement: Pomeron as Reggeized Massive Graviton

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10 Witten Diagram Summation

11 One Graviton in Momentum Representation at High Energy p 1 + p 2 p 3 + p 4

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13 Finite Strong Coupling Pomeron Propagator--Conformal Limit Spin > J ---Use Complex angular momentum representation Reduction to AdS-3

14 { Conformal Invariance AdS-5 Background metric: d 2 z = 1 z 2 0 {dx µ dx µ + d 2 z 0 } Scalar Propagator: S = { } dz { } g M φ(z)g MN N φ(z) + ( d)φ 2 (z) φ (z)φ (w) = G (5) (z, w) { 1 g M gg MN N + ( d) } G (5) (z, w) = δ5 (z w)

15 Complex j-plane: Integration Contour for Mellin Transform J 0 α (t) J-Plane

16 Geometry of Near-Forward Scattering at High Energy Emergence of 5-dim AdS-space Conformal Invariance at High Energy J-AdS3 Representation

17 Emergence of 5-dim AdS-Space Let z=1/r, 0 < z < z0, where z0 ~ 1/Λqcd 17

18 Conformal Invariance at High Energy

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20 Regge in Regge Flat in Space: Flat Space: Diffusion in b

21 Regge Behavior in AdS 5 (Heuristic approach) A s J(t) = s α(0)+α t A t $ - r 2 Fixed branch point in J-plane: Weak coupling: Strong coupling:

22 N = 4 Strong vs Weak BFKL j 0 2 weak 1st Strong weak 2nd αn 22

23 Bulk Degrees of Freedom from Supergravity: Born-Infeld Action 23

24 Flat-Space String Expectations 24

25 Conformal Pomeron and Odderon in Target Space: Ultra-local approximation: 25

26 Diffusion in AdS Flat Space: AdS5, C=+1: AdS5, C=-1: 26

27 Gauge/String Duality C=+1: Pomeron <===> Graviton C=-1: Odderon <===> Kalb-Ramond Field 27

28 J-Plane Structure 28

29 J vs DGLAPP Curves 29

30 Formal Treatment via OPE Flat Space Pomeron Vertex Operator Flat Space Odderon Vertex Operator Pomeron Vertex Operator in AdS Odderon Vertex Operator in AdS 30

31 V. Summary and Outlook Provide meaning for Pomeron/Odderon, etc., non-perturbatively from first principles. Realization of conformal invariance beyond perturbative QCD New starting point for unitarization, saturation, etc. Phenomenological consequences.

32 Gauge/String Dual: Confinement Deformation Use models to provide concrete mathematical realization of Gauge/ String for QCD For simplicity, mostly use Hard- Wall Model Identify model independent features.

33 Cutoff AdS 5 Large Sizes Add Confinement IR wall! String/Glueball

34 Confinement --- Massive Tensor Glueballs Hard-Wall Example: 0 < z 0 < z 1 = 1/Λ Boundary Condition: z1 [z 2 1J 2 (m n z 1 )] = 0 Spectral Representation, discrete spectrum (with mass gap): j=2 G(q, z 0, w 0 ) = (z 0 w 0 ) 2 X n Φ n (z 0 )Φ n (w 0 ) m 2 n t j!2 t = q 2 t

35 Hardwall Regge Spectrum and Cut

36 Summary: QCD String/Gauge Duality in AdS

37 IV. Beyond Pomeron:

38 Eikonal Sum for AdS 38

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