Showing papers by "Miguel S. Costa published in 2008"
TL;DR: In this article, the authors analyze deep inelastic scattering at small Bjorken $x, using the approximate conformal invariance of QCD at high energies, showing that cross sections exhibit geometric scaling and have a simple universal form, which they test against available experimental data for the proton structure function.
Abstract: We analyze deep inelastic scattering at small Bjorken $x$, using the approximate conformal invariance of QCD at high energies. Hard Pomeron exchanges are resummed eikonally, restoring unitarity at large values of the phase shift in the dual anti-de Sitter (AdS) geometry. At weak coupling this phase is imaginary, corresponding to a black disk in AdS space. In this saturated regime, cross sections exhibit geometric scaling and have a simple universal form, which we test against available experimental data for the proton structure function ${F}_{2}(x,{Q}^{2})$. We predict, in particular, the dependence of the cross section on the scaling variable $(Q/{Q}_{\mathrm{s}}{)}^{2}$ in the deeply saturated region, where ${Q}_{\mathrm{s}}$ is the usual saturation scale. We find agreement with current data on ${F}_{2}$ in the kinematical region $0.5l{Q}^{2}l10\text{ }\text{ }{\mathrm{GeV}}^{2}$, $xl{10}^{\ensuremath{-}2}$, with an average 6% accuracy. We conclude by discussing the relation of our approach with the commonly used dipole formalism.
124 citations
TL;DR: In this paper, the authors consider correlators of N = 4 super Yang Mills of the form A similar to, where the operators O-1 and O-2 are scalar primaries.
Abstract: We consider correlators of N = 4 super Yang Mills of the form A similar to , 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.
116 citations
TL;DR: In this article, the authors consider correlators of N=4 super Yang Mills of the form A ~, where the operators O_1 and O_2 are scalar primaries.
Abstract: We consider correlators of N=4 super Yang Mills of the form A ~ , 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.
38 citations
TL;DR: In this article, a six-parameter family of exact, stationary, asymptotically flat solutions of the 4+1 dimensional vacuum Einstein equations with U(1)^2 rotational symmetry was constructed using the inverse scattering method.
Abstract: Using the inverse scattering method we construct a six-parameter family of exact, stationary, asymptotically flat solutions of the 4+1 dimensional vacuum Einstein equations, with U(1)^2 rotational symmetry. It describes the superposition of two Myers-Perry black holes, each with a single angular momentum parameter, both in the same plane. The black holes live in a background geometry which is the Euclidean C-metric with an extra flat time direction. This background possesses conical singularities in two adjacent compact regions, each corresponding to a set of fixed points of one of the U(1) actions in the Cartan sub-algebra of SO(4). We discuss several aspects of the black holes geometry, including the conical singularities arising from force imbalance, and the torsion singularity arising from torque imbalance. The double Myers-Perry solution presented herein is considerably simpler than the four dimensional double Kerr solution and might be of interest in studying spin-spin interactions in five dimensional general relativity.
16 citations
TL;DR: In this article, a six-parameter family of exact, stationary, asymptotically flat solutions of the 4+1 dimensional vacuum Einstein equations with U(1)2 rotational symmetry was constructed using the inverse scattering method.
Abstract: Using the inverse scattering method we construct a six-parameter family of exact, stationary, asymptotically flat solutions of the 4+1 dimensional vacuum Einstein equations, with U(1)2 rotational symmetry. It describes the superposition of two Myers-Perry black holes, each with a single angular momentum parameter, both in the same plane. The black holes live in a background geometry which is the Euclidean C-metric with an extra flat time direction. This background possesses conical singularities in two adjacent compact regions, each corresponding to a set of fixed points of one of the U(1) actions in the Cartan sub-algebra of SO(4). We discuss several aspects of the black holes geometry, including the conical singularities arising from force imbalance, and the torsion singularity arising from torque imbalance. The double Myers-Perry solution presented herein is considerably simpler than the four dimensional double Kerr solution and might be of interest in studying spin-spin interactions in five dimensional general relativity.
11 citations