QCD on the Light-Front

Abstract

Light-Front Hamiltonian theory, derived from the quantization of the QCD Lagrangian at fixed light-front time x + = x 0 + x 3 , provides a rigorous frame-independent framework for solving nonperturbative QCD. The eigenvalues of the light-front QCD Hamiltonian HLF predict the hadronic mass spectrum, and the corresponding eigensolutions provide the light-front wavefunctions which describe hadron structure, providing a direct connection to the QCD Lagrangian. In the semiclassical approximation the valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a single-variable relativistic equation of motion, analogous to the nonrelativistic radial Schrödinger equation, with an effective confining potential U which systematically incorporates the effects of higher quark and gluon Fock states. Remarkably, the potential U has a unique form of a harmonic oscillator potential if one requires that the chiral QCD action remains conformally invariant. A mass gap and the color confinement scale also arises when one extends the formalism of de Alfaro, Fubini and Furlan to light-front Hamiltonian theory. In the case of mesons, the valence Fock-state wavefunctions of HLF for zero quark mass satisfy a single-variable relativistic equation of motion in the invariant variable ζ 2 = b 2 ⊥ x(1−x), which is conjugate to the invariant mass squared M 2 qq . The result is a nonperturbative relativistic light-front quantum mechanical wave equation which incorporates color confinement and other essential spectroscopic and dynamical features of hadron physics, including a massless pion for zero quark mass and linear Regge trajectories M 2 (n, L, S) = 4κ 2 (n+L+S/2) with the same slope in the radial quantum number n and orbital angular momentum L. Only one mass parameter κ appears. The corresponding light-front Dirac equation provides a dynamical and spectroscopic model of nucleons. The same light-front equations arise from the holographic mapping of the soft-wall model modification of AdS5 space with a unique dilaton profile to QCD (3+1) at fixed light-front time. Light-front holography thus provides a precise relation between the bound-state amplitudes in the fifth dimension of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. We also discuss the implications of the underlying conformal template of QCD for renormalization scale-setting and the implications of light-front quantization for the value of the cosmological constant.

Cubic interaction vertices for continuous-spin fields and arbitrary spin massive fields

“…Various interesting applications of the light-cone formalism to field theories such as QCD are discussed in refs. [24][25][26].…”

Nucleon and flavor form factors in a light front quark model in AdS/QCD

“…So, the confining potential for baryons cannot be produced by dilaton and is put in by hand in the soft wall model. The form of the confining potential (κ 4 ζ 2 ) is unique for both the meson and baryon sectors [31]. The twist-3 nucleon wave functions in the soft wall model are obtained as…”

Holography as a gauge phenomenon in Higher Spin duality

“…A similar identification of AdS space in light-cone QCD was developed in [22,23]. In addition a renormalization group method for bi-local observables is being developed in [24][25][26][27].…”