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Low-x physics in AdS/CFT

Low-x physics in AdS/CFT. Yoshitaka Hatta (Saclay). with E. Iancu and A. Mueller. Motivations. It’s interesting !...though it may have little (if any) relevance to real experiments… Longstanding problems in the Regge regime of QCD

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Low-x physics in AdS/CFT

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  1. Low-x physics in AdS/CFT Yoshitaka Hatta (Saclay) with E. Iancu and A. Mueller

  2. Motivations • It’s interesting !...though it may have little (if any) relevance to real experiments… • Longstanding problems in the Regge regime of QCD (Froissart’s theorem, soft vs. hard Pomerons, etc.) Theorists desperate for new ideas and insights from ``QCD—like’’ theories. • Possible application to the ``sQGP’’ (Finite—T )

  3. N=4 Super Yang-Mills • SU(Nc) local gauge symmetry • Maximally supersymmetric gauge theory in D=4. • Conformal symmetry SO(4,2) The t`Hooft coupling doesn’t run. • Global SU(4) R-symmetry

  4. Type IIB superstring • Consistent superstring theory in D=10 • 256 massless states (supergravity modes) • Admits the black brane solution which is asymptotically AdS `radius’ coordinate Our universe

  5. The correspondence Maldacena, `97 • Take the limits and • N=4 SYM at strong coupling is dual to weak coupling type IIB on AdS • Spectrums of the two theories match CFT string (anomalous) dimension mass t`Hooft parameter curvature radius number of colors string coupling constant

  6. Application to DIS Polchinski, Strassler, `02 R-charge current excites metric fluctuations in the bulk, which then scatters off a dilaton (`glueball’) via the super Virasoro-Shapiro amplitude. We are here Photon localized at large Dilaton localized at small Cut off the space at (mimic confinement)

  7. The string S-matrix Flat space Virasoro-Shapiro t-channel graviton pole AdS case Laplacian in the 5th direction causes the shift of the intercept as well as diffusion. Gravitons become massive c.f. BFKL Kotikov, Lipatov, Onishchenko, Velizhanin `04 Brower, Polchinski, Strassler, Tan `06

  8. Beyond the single Pomeron approximation • Graviton dominance — high energy behavior even worse than in QCD. • No problem as long as • Keep Nc finite and study the onset of unitarity corrections. Multiple Pomeron exchange String loop diagrams

  9. Saturation saddle point at weak coupling Amplitudes factorize in the kt-space BFKL saddle point Saturation saddle point determined from 1

  10. ``Saturation’’ saddle point at strong coupling Amplitudes factorize in the r-space

  11. Anomalous dimension in N=4 SYM The characteristic function extremely flat ``Saturation’’ anomalous dimension huge  Anomalous dimension of the twist—two operator Gubser, Klebanov, Polyakov, `02 ``Diffusion approximation’’ is related to the Regge behavior of string excited states  Valid in a broad region, unlike BFKL !

  12. The real part strikes back At large massless gravitons reemerge. small large 2 4 6 2 4 6 The real part reaches the unitarity limit first.  Resum by the eikonal approximation t`Hooft, `87

  13. Phase diagram at weak coupling Saturation Single Pomeron

  14. Phase diagram at strong coupling ~ Black hole Inelastic Diffraction Eikonal Single Pomeron

  15. Photon virtuality as an impact parameter Compare our result with Amati, Ciafaloni, Veneziano `87 (working in 10D string theory !) string size elastic amplitude reaches unity inelastic amplitude reaches unity diffractive absorption reaches unity effective string size

  16. Conclusions • Regge regime in AdS/CFT largely unexplored. • Some similarities, striking differences w.r.t. weak coupling QCD. • Amati, Ciafaloni, Veneziano scenario realized in gauge theory • Strong gravity and black hole creation  Reminiscent of the nonlinear effects in QCD in the saturation regime

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