AdS/QCD, Light-Front Holography, and Sublimated Gluons

Gauge/gravity duality leads to a simple, analytical, and phenomenologically compelling nonperturbative approximation to the full light-front QCD Hamiltonian. This approach, called "Light-Front Holography", successfully describes the spectroscopy of light-quark meson and baryons, their elastic and transition form factors, and other hadronic properties. The bound-state Schrodinger and Dirac equations of the soft-wall AdS/QCD model predict linear Regge trajectories which have the same slope in orbital angular momentum L and radial quantum number n for both mesons and baryons. Light-front holography connects the fifth-dimensional coordinate of AdS space z to an invariant impact separation variable zeta in 3+1 space at fixed light-front time. A key feature is the determination of the frame-independent light-front wavefunctions of hadrons -- the relativistic analogs of the Schrodinger wavefunctions of atomic physics which allow one to compute form factors, transversity distributions, spin properties of the valence quarks, jet hadronization, and other hadronic observables. One thus obtains a one-parameter color-confining model for hadron physics at the amplitude level. AdS/QCD also predicts the form of a non-perturbative effective running coupling and its beta-function with an infrared fixed point which agrees with the effective coupling extracted from measurements of the Bjorken sum rule below 1 GeV^2. This is consistent with a flux-tube interpretation of QCD where soft gluons are sublimated into a color-confining potential for quarks. We discuss a number of phenomenological hadronic properties which support this picture.Comment: Invited talk, presented by SJB at the International Workshop on QCD Green's Functions, Confinement and Phenomenology, 5-9 September 2011, Trento, Ital

AdS/QCD, Light-Front Holography, and Color Confinement

A remarkable holographic feature of dynamics in AdS space in five dimensions is that it is dual to Hamiltonian theory in physical space-time, quantized at fixed light-front time {\tau} = t+z/c. This light-front holographic principle provides a precise relation between the bound-state amplitudes in AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. The fifth dimension coordinate z is dual to the light front variable {\zeta} describing the invariant separation of the quark constituents. The resulting valence Fock-state wavefunction eigensolutions of the light-front QCD Hamiltonian satisfy a single-variable relativistic equation of motion, analogous to the nonrelativistic radial Schr\"odinger equation. The soft-wall dilaton profile exp ({\kappa}^2 {\zeta}^2) provides a model for the light-front potential which is color-confining and reproduces well the linear Regge behavior of the light-quark hadron spectrum in both L, the orbital angular momentum, and n, the radial node number. The pion mass vanishes in the chiral limit and other features of chiral symmetry are satisfied. The resulting running QCD coupling displays an infrared fixed point. The elastic and transition form factors of the pion and the nucleons are also found to be well described in this framework. The light-front AdS/QCD holographic approach thus gives a frame-independent analytic first approximation of the color-confining dynamics, spectroscopy, and excitation spectra of relativistic light-quark bound states in QCD.Comment: Contribution to the Proceedings of the conference, Xth Quark Confinement and the Hadron Spectrum, October 8-12, 2012, TUM Campus Garching, Munich, German

QCD on the Light-Front -- A Systematic Approach to Hadron Physics

Light-Front Hamiltonian theory provides a rigorous frame-independent framework for solving nonperturbative QCD. The valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a single-variable relativistic equation of motion, analogous to the nonrelativistic radial Schr\"odinger 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 arises when one extends the formalism of de Alfaro, Fubini and Furlan to light-front Hamiltonian theory. The valence LF meson wavefunctions for zero quark mass satisfy a single-variable relativistic equation of motion in the invariant variable $\zeta^2=b^2_\perp x(1-x)$, which is conjugate to the invariant mass squared. 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 with the same slope in the radial quantum number n and orbital angular momentum L. The corresponding light-front Dirac equation provides a model of nucleons. The same light-front equations arise from the holographic mapping of the soft-wall model modification of AdS_5 space with a unique dilaton profile to QCD (3+1) at fixed light-front time. Light-front holography thus provides a precise relation between amplitudes in the fifth dimension of AdS space and light-front wavefunctions. 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.Comment: Invited talk, presented by SJB at LightCone 2013+, May 20- May 24, 2013, Skiathos, Greece. arXiv admin note: text overlap with arXiv:1309.4856, arXiv:1308.5251, arXiv:1302.539

Light-Front Holographic QCD and the Confinement Potential

Light-Front Hamiltonian theory, derived from the quantization of the QCD Lagrangian at fixed light-front time \tau = t+z/c, provides a rigorous frame-independent framework for solving nonperturbative QCD. The eigenvalues of the light-front QCD Hamiltonian predict the hadronic mass spectrum, and the eigensolutions provide the light-front wavefunctions describing hadron structure. The valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a single-variable relativistic equation of motion, analogous to the nonrelativistic radial Schrodinger equation, with an effective confining potential U which systematically incorporates the effects of higher quark and gluon Fock states. The potential U has a unique form if one requires that the action for zero quark mass remains conformally invariant. The holographic mapping of gravity in AdS space to QCD with a specific soft-wall dilaton yields the same light-front Schrodinger equation. It also gives a precise relation between the bound-state amplitudes in the fifth dimension z of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. The elastic and transition form factors of the pion and the nucleons are found to be well described in this framework. The predictions include a zero-mass pion in the chiral limit, and linear Regge trajectories with the same slope in the radial quantum number n and orbital angular momentum L. The light-front AdS/QCD holographic approach thus gives a frame-independent representation of color-confining dynamics and the excitation spectra of light-quark hadrons in terms of a single mass parameter. 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.Comment: Presented by SJB at Light-Cone 2012: Relativistic Hadronic and Particle Physics, 10 to 15 December, 2012 at the University of Delhi, New Delhi, Indi