Supersymmetry across the Hadronic Spectrum

Semiclassical light-front bound-state equations for hadrons are presented and compared with experiment. The essential dynamical feature is the holographic approach; that is, the hadronic equations in four-dimensional Minkowski space are derived as holograms of classical equations in a 5-dimensional anti-de Sitter space. The form of the equations is constrained by the imposed superconformal algebra, which fixes the form of the light-front potential. If conformal symmetry is strongly broken by heavy quark masses, the combination of supersymmetry and the classical action in the 5-dimensional space still fixes the form of the potential. By heavy quark symmetry, the strength of the potential is related to the heavy quark mass. The contribution is based on several recent papers in collaboration with Stan Brodsky and Guy de Téramond

Hadron Spectroscopy and Dynamics from Light-Front Holography and Conformal Symmetry

To a first semiclassical approximation one can reduce the multi-parton light-front problem in QCD to an effective one-dimensional quantum field theory, which encodes the fundamental conformal symmetry of the classical QCD Lagrangian. This procedure leads to a relativistic light-front wave equation for arbitrary spin which incorporates essential spectroscopic and non-perturbative dynamical features of hadron physics. The mass scale for confinement and higher dimensional holographic mapping to AdS space are also emergent properties of this framework.Comment: 11 pages, 6 figures. Invited plenary talk, presented by GdT at the 13th International Conference on Meson-Nucleon Physics and the Structure of the Nucleon (MENU 2013), Rome, September 30 - October 4, 201

Light-Front Holographic Quantum Chromodynamics

Anti-de Sitter space in five dimensions provides an exact geometrical representation of the conformal group. Remarkably, gravity in AdS$_5$ space is holographically dual to frame-independent light-front Hamiltonian theory, derived from the quantization of the QCD Lagrangian at fixed light-front time $\tau = x^0+x^3$. Light-front holography also leads to a precise relation between the bound-state amplitudes in the fifth dimension $z$ of AdS space and the variable $\zeta$, where $\zeta^2 = b^2_\perp x(1-x)$ is the argument of the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. The holographic mapping of AdS space with a specific "soft-wall" dilaton yields a confining potential $U(\zeta^2)$ for the light-front Schr\"odinger equation for hadrons with arbitrary spin $J$. Remarkably, $U(\zeta^2)$ has a unique form of a harmonic oscillator potential if one requires that the chiral QCD action remains conformally invariant. One thus obtains an effective light-front effective theory for general spin which respects the conformal symmetry of the four-dimensional classical QCD Lagrangian. The predictions of the LF equations of motion include a zero-mass pion in the chiral $m_q\to 0$ limit, and linear Regge trajectories $M^2(n,L) \propto n+L$ with the same slope in the radial quantum number $n$ and the orbital angular momentum $L$. The light-front AdS/QCD holographic approach gives a frame-independent representation of color-confining dynamics, Regge spectroscopy, as well as the excitation spectra of relativistic light-quark meson and baryon bound states in QCD in terms of a single mass parameter. We also briefly 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 the International Conference on Nuclear Theory in the Supercomputing Era (NTSE 2013) in honor of James Vary, May 13 - May 17, 2013, Iowa State University, Ames, Iow