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Low-x physics in AdS/CFT

This study explores the Regge regime of QCD and its relevance to experiments, focusing on AdS/CFT and its application to the strong coupling limit of N=4 SYM. The paper investigates the similarities and differences between weak coupling QCD and AdS/CFT, with potential implications for the quark-gluon plasma. It also examines the role of gravity and black hole creation in AdS/CFT.

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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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