AdS/QCD, Light-Front Holography, and the Nonperturbative Running Coupling

Abstract

The combination of Anti-de Sitter space (AdS) methods with light-front (LF) holography provides a remarkably accurate first approximation for the spectra and wavefunctions of meson and baryon light-quark bound states. The resulting bound-state Hamiltonian equation of motion in QCD leads to relativistic light-front wave equations in terms of an invariant impact variable $\zeta$ which measures the separation of the quark and gluonic constituents within the hadron at equal light-front time. These equations of motion in physical space-time are equivalent to the equations of motion which describe the propagation of spin-$J$ modes in anti--de Sitter (AdS) space. The eigenvalues give the hadronic spectrum, and the eigenmodes represent the probability distributions of the hadronic constituents at a given scale. A positive-sign confining dilaton background modifying AdS space gives a very good account of meson and baryon spectroscopy and form factors. The light-front holographic mapping of this model also leads to a non-perturbative effective coupling ${\alpha }_s^{AdS}(Q^2)$ which agrees with the effective charge defined by the Bjorken sum rule and lattice simulations. It displays a transition from perturbative to nonperturbative conformal regimes at a momentum scale $\sim 1$ GeV. The resulting $\beta$-function appears to capture the essential characteristics of the full $\beta$-function of QCD, thus giving further support to the application of the gauge/gravity duality to the confining dynamics of strongly coupled QCD.

Invited talk, presented by SJB at SCGT09, 2009 International Workshop on Strong Coupling Gauge Theories in the LHC Era, Nagoya, December 8-11, 2009, updated figure

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