The AdS/CFT Correspondence and Light-Front QCD

TL;DR

This paper develops a frame-independent light-front Schrödinger equation for QCD, derived from the AdS/CFT correspondence, enabling a relativistic, holographic description of hadrons and their wavefunctions.

Contribution

It introduces an invariant light-front coordinate and a holographic approach that maps AdS space modes to physical hadron wavefunctions, advancing the understanding of hadronic structure in QCD.

Findings

Derivation of a single-variable light-front Schrödinger equation for QCD.

Establishment of a holographic mapping between AdS modes and hadron wavefunctions.

Framework for systematic improvements and hadronization calculations at the amplitude level.

Abstract

We identify an invariant light-front coordinate $\zeta$ which allows the separation of the dynamics of quark and gluon binding from the kinematics of constituent spin and internal orbital angular momentum. The result is a single-variable light-front Schrodinger equation for QCD which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum. This frame-independent light-front wave equation is equivalent to the equations of motion which describe the propagation of spin-$J$ modes on anti-de Sitter (AdS) space. Light-front holography is a remarkable feature of AdS/CFT: it allows hadronic amplitudes in the AdS fifth dimension to be mapped to frame-independent light-front wavefunctions of hadrons in physical space-time, thus providing a relativistic description of hadrons at the amplitude level. In principle, the model can be systematically improved by diagonalizing the full QCD light-front Hamiltonian on the AdS/QCD basis. Quark and gluon hadronization can be computed at the amplitude level by convoluting the off-shell $T$ matrix calculated from the QCD light-front Hamiltonian with the hadronic light-front wavefunctions. We also note the distinction between static observables such as the probability distributions computed from the square of the light-front wavefunctions versus dynamical observables such as the structure functions and the leading-twist single-spin asymmetries measured in deep inelastic scattering which include the effects of initial and final-state interactions.