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 ${\zeta }^2=b_{\perp }^{2}x(1-x)$ 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 $M^2(n,L) \propto n+L$withthesameslopeintheradialquantumnumber$n$ 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.