AdS/QCD and Applications of Light-Front Holography

Light-front holography leads to a rigorous connection between hadronic amplitudes in a higher dimensional anti-de Sitter(AdS) space and frame-independent light-front wavefunctions of hadrons in(3 + 1)-dimensional physical space-time,thus providing a compelling physical interpretation of the AdS/CFT correspondence principle and AdS/QCD,a useful framework which describes the correspondence between theories in a modified AdS 5 background and confining field theories in physical space-time.To a first semiclassical approximation,where quantum loops and quark masses are not included,this approach leads to a single-variable light-front Schro¨dinger equation which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum.The coordinate z in AdS space is uniquely identified with a Lorentz-invariant coordinate ζ which measures the separation of the constituents within a hadron at equal light-front time.The internal structure of hadrons is explicitly introduced and the angular momentum of the constituents plays a key role.We give an overview of the light-front holographic approach to strongly coupled QCD.In particular,we study the photon-to-meson transition form factors(TFFs) FMγ(Q 2) for γ→ M using light-front holographic methods.The results for the TFFs for the η and η ' mesons are also presented.Some novel features of QCD are discussed,including the consequences of confinement for quark and gluon condensates.A method for computing the hadronization of quark and gluon jets at the amplitude level is outlined.

AdS/QCD and light front holography: A new approximation to QCD

The combination of Anti-de Sitter space （AdS） methods with light-front holography leads to a semi-classical first approximation to the spectrum and wavefunctions of meson and baryon light-quark bound states.Starting from the bound-state Hamiltonian equation of motion in QCD,we derive relativistic lightfront wave equations in terms of an invariant impact variable ζ 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.Its eigenvalues give the hadronic spectrum,and its eigenmodes represent the probability distributions of the hadronic constituents at a given scale.Applications to the light meson and baryon spectra are presented.The predicted meson spectrum has a string-theory Regge form M^ 2 = 4κ ^2 （n＋L＋S/2）;i.e.,the square of the eigenmass is linear in both L and n,where n counts the number of nodes of the wavefunction in the radial variable ζ.The space-like pion and nucleon form factors are also well reproduced.One thus obtains a remarkable connection between the description of hadronic modes in AdS space and the Hamiltonian formulation of QCD in physical space-time quantized on the light-front at fixed light-front time τ.The model can be systematically improved by using its complete orthonormal solutions to diagonalize the full QCD lightfront Hamiltonian or by applying the Lippmann-Schwinger method in order to systematically include the QCD interaction terms.