Kinematical and Dynamical Aspects of Higher-Spin Bound-State Equations in Holographic QCD

In this paper we derive holographic wave equations for hadrons with arbitrary spin starting from an effective action in a higher-dimensional space asymptotic to anti-de Sitter (AdS) space. Our procedure takes advantage of the local tangent frame, and it applies to all spins, including half-integer spins. An essential element is the mapping of the higher-dimensional equations of motion to the light-front Hamiltonian, thus allowing a clear distinction between the kinematical and dynamical aspects of the holographic approach to hadron physics. Accordingly, the non-trivial geometry of pure AdS space encodes the kinematics, and the additional deformations of AdS space encode the dynamics, including confinement. It thus becomes possible to identify the features of holographic QCD which are independent of the specific mechanisms of conformal symmetry breaking. In particular, we account for some aspects of the striking similarities and differences observed in the systematics of the meson and baryon spectra.Comment: 43 page

Threefold Complementary Approach to Holographic QCD

A complementary approach, derived from (a) higher dimensional anti--de Sitter (AdS) space, (b) light-front quantization and (c) the invariance properties of the full conformal group in one dimension leads to a nonperturbative relativistic light-front wave equation which incorporates essential spectroscopic and dynamical features of hadron physics. The fundamental conformal symmetry of the classical QCD Lagrangian in the limit of massless quarks is encoded in the resulting effective theory. The mass scale for confinement emerges from the isomorphism between the conformal group and SO(2,1). This scale appears in the light-front Hamiltonian by mapping to the evolution operator in the formalism of de Alfaro, Fubini and Furlan, which retains the conformal invariance of the action. Remarkably, the specific form of the confinement interaction and the corresponding modification of AdS space are uniquely determined in this procedure.Comment: Reference added. Article accepted for publication in PL

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

Conformal Symmetry, Confinement, and Light-Front Holographic QCD

We show that (a) the conformal properties of Anti-de Sitter (AdS) space, (b) the properties of a field theory in one dimension under the full conformal group found by de Alfaro, Fubini and Furlan, and (c) the frame-independent single-variable light-front Schr\"odinger equation for bound states all lead to the same result: a relativistic nonperturbative model which successfully incorporates salient features of hadronic physics, including confinement, linear Regge trajectories, and results which are conventionally attributed to spontaneous chiral symmetry breaking.Comment: Presented by SJB at the Third Workshop on the QCD Structure of the Nucleon (QCD-N'12), Bilbao, Spain, October 22-26, 2012. This work was supported by the Department of Energy contract DE--AC02--76SF0051

Modified Anti-de-Sitter Metric, Light-Front Quantized QCD, and Conformal Quantum Mechanics

We briefly review the remarkable connections between light-front QCD, gravity in AdS space, and conformal quantum mechanics. We discuss, in particular, the group theoretical and geometrical aspects of the underlying one-dimensional quantum field theory. The resulting effective theory leads to a phenomenologically successful confining interaction potential in the relativistic light-front wave equation which incorporates relevant non-perturbative dynamical aspects of hadron physics.Comment: 12 pages, 2 figures. Presented by HGD at the International Fall Workshop Geometry and Physics II, Institut Henri Poincare, Paris, November 28 and 29, 201