Holographic light-front QCD

TL;DR

This work surveys holographic light-front QCD (HLFQCD), where the holographic coordinate $z$ is identified with the light-front separation $\zeta$ to produce a semiclassical hadron Hamiltonian. A graded superconformal quantum-mechanical framework fixes the confinement mechanism, introducing a scale $\lambda$ and yielding a meson–baryon supersymmetry with $L_M=L+1$, $L_B=L$, and a harmonic-like confinement $U_{AdS}(z)$. The approach delivers concrete, parameter-light predictions for hadron masses $M_M^2$ and $M_B^2$, linear Regge trajectories with slope $\alpha' = 1/(4\lambda)$, and consistent form factors and parton distributions via a universal function $w(x)$, including a Pomeron-based description of gluons and a DIS entanglement-entropy relation. It also connects nonperturbative holographic insights to perturbative QCD through a scale-dependent effective coupling, highlighting a unified picture that echoes Regge/Veneziano structure and provides predictive hadron phenomenology across scales.

Abstract

This brief review presents the key components of light-front holographic quantum chromodynamics (HLFQCD). Particular attention is given to the introduction of the QCD color confinement scale within the context of a graded superconformal algebra. A concise overview of applications is provided, including spectroscopy, form factors, parton distributions of hadrons, and the relationship between entanglement entropy and high-energy scattering. While many other recent applications of HLFQCD exist in the literature, they are not included in this short overview of our latest work.

Figures (5)

• Figure 1: Light meson and baryon trajectories as a function of the LF orbital angular momentum $L$. The dash curves are the prediction of HLFQCD for the confinement scale $\sqrt{\lambda_M}= \sqrt{\lambda_B} = 0.52$ GeV. Finite quark masses are included by a perturbative term Brodsky:2014yha .
• Figure 2: The HLFQCD model predicts boson resonances that lie on linear Regge trajectories. The model predictions for light vector mesons with intrinsic quark spin $s_M=1$ (and isospin $I=1$) are shown as empty circles with the corresponding quantum numbers. Confirmed resonances PDG are represented as full circles. The leading trajectory (red) generates the the $\rho-a$ Reggeon exchange in charge exchange pion-nucleon scattering (right), with the trajectory given by $\alpha(t)=f_M(t,0), n=0, s_M=1$. The daughter trajectories (grey), correspond to $n = 1, 2, \cdots$. These trajectories have no noticeable influence on the total cross sections at high energies due to their lower intercepts. The intercept $\alpha_{\rho}(0)$ can be extracted from the energy dependence of the cross section, $\sigma(s) \sim (s/s_0)^{\alpha_{\rho}(0)}$, and has a value close to 0.5.
• Figure 3: Parton distribution functions in the proton and pion obtained in the present approach (red bands), compared with several global fits. The results shown for the quark PDFs, $x q(x)$, are obtained by evolving the initial intrinsic distributions at the hadronic scale $\mu^2_0 \simeq 1$ GeV$^2$ to $\mu^2 = 27$ GeV$^2$ to compare with experimental results (top figures); from deTeramond:2018ecg. Comparison for the gluon gPDFs predictions, $x g(x)$, are evolved to $\mu^2 = 10$ GeV$^2$ (bottom figures); from deTeramond:2021lxc.
• Figure 4: a) The Pomeron intercept extracted from the gluon distribution functions of the pion and proton compared with the intercept extracted from $\gamma^*(Q^2)\, p$ cross section. b) Electroproduction off protons. The total cross section $\sigma(s,Q^2) \sim s^{\alpha_P-1}$ (structure function $F_2$) can be measured in the electroproduction process $e+ p \to e'+X$ with $Q^2=-(p_{e'}-p_e)^2,\; s= (p_p +p_e-p_{e'})^2$.
• Figure 5: The effective coupling $\alpha_{\rm eff}(Q)$. According to (\ref{['gen']}) with a fixed value $\lambda=\kappa^2 = 0.286$ GeV$^2$ (left) and with a $Q$-dependent value $\lambda(Q^2)= \kappa^2(Q^2)$; see deTeramond:2025qlj.