Holography from Conformal Field Theory

The locality of bulk physics at distances below the AdS length is one of the remarkable aspects of AdS/CFT duality, and one of the least tested. It requires that the AdS radius be large compared to the Planck length and the string length. In the CFT this implies a large-N expansion and a gap in the spectum of anomalous dimensions. We conjecture that the implication also runs in the other direction, so that any CFT with a planar expansion and a large gap has a local bulk dual. For an abstract CFT we formulate the consistency conditions, most notably crossing symmetry, and show that the conjecture is true in a broad range of CFT's, to first nontrivial order in 1/N^2: any CFT with a gap and a planar expansion is generated via the AdS/CFT dictionary from a local bulk interaction. We establish this result by a counting argument on each side, and also investigate various properties of some explicit solutions.Comment: 49 pages. Minor corrections. Figure and references adde

Open-String Actions and Noncommutativity Beyond the Large-B Limit

In the limit of large, constant B-field (the ``Seiberg-Witten limit''), the derivative expansion for open-superstring effective actions is naturally expressed in terms of the symmetric products *n. Here, we investigate corrections around the large-B limit, for Chern-Simons couplings on the brane and to quadratic order in gauge fields. We perform a boundary-state computation in the commutative theory, and compare it with the corresponding computation on the noncommutative side. These results are then used to examine the possible role of Wilson lines beyond the Seiberg-Witten limit. To quadratic order in fields, the entire tree-level amplitude is described by a metric-dependent deformation of the *2 product, which can be interpreted in terms of a deformed (non-associative) version of the Moyal * product.Comment: 30 pages, harvma

AdS black disk model for small-x DIS

Using the approximate conformal invariance of QCD at high energies we consider a simple AdS black disk model to describe saturation in DIS. Deep inside saturation the structure functions have the same power law scaling, F_T ~ F_L ~ 1/x^w, where w is related to the expansion rate of the black disk with energy. Furthermore, the ratio F_L /F_T is given by the universal value (1+w)/(3+w), independently of the target. For virtual photon-photon scattering at high energies we obtain explicit expressions and ratios for the total cross sections of transverse and longitudinal photons in terms of the single parameter w.Comment: 5 pages. Minor correction

Writing CFT correlation functions as AdS scattering amplitudes

We explore the Mellin representation of conformal correlation functions recently proposed by Mack. Examples in the AdS/CFT context reinforce the analogy between Mellin amplitudes and scattering amplitudes. We conjecture a simple formula relating the bulk scattering amplitudes to the asymptotic behavior of Mellin amplitudes and show that previous results on the flat space limit of AdS follow from our new formula. We find that the Mellin amplitudes are particularly useful in the case of conformal gauge theories in the planar limit. In this case, the four point Mellin amplitudes are meromorphic functions whose poles and their residues are entirely determined by two and three point functions of single-trace operators. This makes the Mellin amplitudes the ideal objects to attempt the conformal bootstrap program in higher dimensions.Comment: 23 pages + appendice

Deep Inelastic Scattering in Conformal QCD

We consider the Regge limit of a CFT correlation function of two vector and two scalar operators, as appropriate to study small-x deep inelastic scattering in N=4 SYM or in QCD assuming approximate conformal symmetry. After clarifying the nature of the Regge limit for a CFT correlator, we use its conformal partial wave expansion to obtain an impact parameter representation encoding the exchange of a spin j Reggeon for any value of the coupling constant. The CFT impact parameter space is the three-dimensional hyperbolic space H3, which is the impact parameter space for high energy scattering in the dual AdS space. We determine the small-x structure functions associated to the exchange of a Reggeon. We discuss unitarization from the point of view of scattering in AdS and comment on the validity of the eikonal approximation. We then focus on the weak coupling limit of the theory where the amplitude is dominated by the exchange of the BFKL pomeron. Conformal invariance fixes the form of the vector impact factor and its decomposition in transverse spin 0 and spin 2 components. Our formalism reproduces exactly the general results predict by the Regge theory, both for a scalar target and for gamma*-gamma* scattering. We compute current impact factors for the specific examples of N=4 SYM and QCD, obtaining very simple results. In the case of the R-current of N=4 SYM, we show that the transverse spin 2 component vanishes. We conjecture that the impact factors of all chiral primary operators of N=4 SYM only have components with 0 transverse spin.Comment: 44+16 pages, 7 figures. Some correction

Description of LHC data in a soft interaction model

We show in this paper that we have found a set of parameters in our model for the soft interactions at high energy, that successfully describes all high energy experimental data, including the LHC data. This model is based on a single Pomeron with large intercept \Delta_\pom = 0.23 and slope \alpha'_\pom = 0, that describes both long and short distance processes. It also provides a natural matching with perturbative QCD. All features of our model are similar to the expectations of N=4 SYM, which at present is the only theory that is able to treat srong interactions on a theoretical basis.Comment: 11 pages with 7 figures in eps format

Eikonal Methods in AdS/CFT: BFKL Pomeron at Weak Coupling

We consider correlators of N=4 super Yang Mills of the form A ~ < O_1 O_2 O*_1 O*_2 >, where the operators O_1 and O_2 are scalar primaries. In particular, we analyze this correlator in the planar limit and in a Lorentzian regime corresponding to high energy interactions in AdS. The planar amplitude is dominated by a Regge pole whose nature varies as a function of the 't Hooft coupling g^2. At large g, the pole corresponds to graviton exchange in AdS, whereas at weak g, the pole is that of the hard perturbative BFKL pomeron. We concentrate on the weak coupling regime and analyze pomeron exchange directly in position space. The analysis relies heavily on the conformal symmetry of the transverse space E^2 and of its holographic dual hyperbolic space H_3, describing with an unified language, both the weak and strong 't Hooft coupling regimes. In particular, the form of the impact factors is highly constrained in position space by conformal invariance. Finally, the analysis suggests a possible AdS eikonal resummation of multi-pomeron exchanges implementing AdS unitarity, which differs from the usual 4-dimensional eikonal exponentiation. Relations to violations of 4-dimensional unitarity at high energy and to the onset of nonlinear effects and gluon saturation become immediate questions for future research.Comment: 42 pages, 13 figure

Glauber - Gribov approach for DIS on nuclei in N=4 SYM

In this paper the Glauber-Gribov approach for deep-inelastic scattering (DIS) with nuclei is developed in N=4 SYM. It is shown that the amplitude displays the same general properties, such as geometrical scaling, as is the case in the high density QCD approach. We found that the quantum effects leading to the graviton reggeization, give rise to an imaginary part of the nucleon amplitude, which makes the DIS in N=4 SYM almost identical to the one expected in high density QCD. We concluded that the impact parameter dependence of the nucleon amplitude is very essential for N=4 SYM, and the entire kinematic region can be divided into three regions which are discussed in the paper. We revisited the dipole description for DIS and proposed a new renormalized Lagrangian for the shock wave formalism which reproduces the Glauber-Gribov approach in a certain kinematic region. However the saturation momentum turns out to be independent of energy, as it has been discussed by Albacete, Kovchegov and Taliotis. We discuss the physical meaning of such a saturation momentum $Q_s(A)$ and argue that one can consider only $Q>Q_s(A)$ within the shock wave approximation.Comment: 40pp.,9 figures in eps file

High Energy Bounds on Soft N=4 SYM Amplitudes from AdS/CFT

Using the AdS/CFT correspondence, we study the high-energy behavior of colorless dipole elastic scattering amplitudes in N=4 SYM gauge theory through the Wilson loop correlator formalism and Euclidean to Minkowskian analytic continuation. The purely elastic behavior obtained at large impact-parameter L, through duality from disconnected AdS_5 minimal surfaces beyond the Gross-Ooguri transition point, is combined with unitarity and analyticity constraints in the central region. In this way we obtain an absolute bound on the high-energy behavior of the forward scattering amplitude due to the graviton interaction between minimal surfaces in the bulk. The dominant "Pomeron" intercept is bounded by alpha less than or equal to 11/7 using the AdS/CFT constraint of a weak gravitational field in the bulk. Assuming the elastic eikonal approximation in a larger impact-parameter range gives alpha between 4/3 and 11/7. The actual intercept becomes 4/3 if one assumes the elastic eikonal approximation within its maximally allowed range L larger than exp{Y/3}, where Y is the total rapidity. Subleading AdS/CFT contributions at large impact-parameter due to the other d=10 supergravity fields are obtained. A divergence in the real part of the tachyonic KK scalar is cured by analyticity but signals the need for a theoretical completion of the AdS/CFT scheme.Comment: 25 pages, 3 eps figure

Intersecting S-Brane Solutions of D=11 Supergravity

We construct all possible orthogonally intersecting S-brane solutions in 11-dimensions corresponding to standard supersymmetric M-brane intersections. It is found that the solutions can be obtained by multiplying the brane and the transverse directions with appropriate powers of two hyperbolic functions of time. This is the S-brane analog of the ``harmonic function rule''. The transverse directions can be hyperbolic, flat or spherical. We also discuss some properties of these solutions.Comment: 12 pages, Latex, a reference adde