Light-Front Holography and Superconformal Quantum Mechanics: A New Approach to Hadron Structure and Color Confinement

Abstract

A primary question in hadron physics is how the mass scale for hadrons consisting of light quarks, such as the proton, emerges from the QCD Lagrangian even in the limit of zero quark mass. If one requires the effective action which underlies the QCD Lagrangian to remain conformally invariant and extends the formalism of de Alfaro, Fubini and Furlan to light-front Hamiltonian theory, then a unique, color-confining potential with a mass parameter $\kappa$ emerges. The actual value of the parameter $\kappa$ is not set by the model - only ratios of hadron masses and other hadronic mass scales are predicted. The result is a nonperturbative, relativistic light-front quantum mechanical wave equation, the Light-Front Schrödinger 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 identical slope in the radial quantum number $n$ and orbital angular momentum $L$. The same light-front equations for mesons with spin $J$ also can be derived from the holographic mapping to QCD (3+1) at fixed light-front time from the soft-wall model modification of AdS${}_5$ space with a specific dilaton profile. 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. One can also extend the analysis to baryons using superconformal algebra - $2\times 2$ supersymmetric representations of the conformal group. The resulting fermionic LF bound-state equations predict striking similarities between the meson and baryon spectra. In fact, the holographic QCD light-front Hamiltonians for the states on the meson and baryon trajectories are identical if one shifts the internal angular...

17 pages, 8 figures. Contribution to the proceedings of Hadron Structure'15, Slovakia. Talk presented by S. J. Brodsky

References in corpus (8)

• Light-Front Dynamics and AdS/QCD Correspondence: The Pion Form Factor in the Space- and Time-Like Regions
• Basic features of the pion valence-quark distribution function
• Baryon Spectrum from Superconformal Quantum Mechanics and its Light-Front Holographic Embedding
• Determination of the effective strong coupling constant alpha_{s,g_1}(Q^2) from CLAS spin structure function data
• Kinematical and Dynamical Aspects of Higher-Spin Bound-State Equations in Holographic QCD
• Effective confining potentials for QCD
• The Light-Front Schrödinger Equation and Determination of the Perturbative QCD Scale from Color Confinement
• Recursion relations for multi-gluon off-shell amplitudes on the light-front and Wilson lines

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• Solving the Wrong Hierarchy Problem
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• High Resolution Nonperturbative Light-Front Simulations of the True Muonium Atom
• Do we understand the internal spaces of second quantized fermion and boson fields, with gravity included? Relation with strings theories
• Quark mass matrices inspired by a numerical relation
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