Superconformal Baryon-Meson Symmetry and Light-Front Holographic QCD

TL;DR

This paper develops a superconformal algebra-based light-front Hamiltonian for mesons and baryons, revealing a supersymmetric relation between their spectra and providing insights into confinement and chiral symmetry breaking in QCD.

Contribution

It introduces a superconformal algebra framework to unify meson and baryon spectra in light-front QCD, connecting them through supersymmetry and deriving an effective confinement potential.

Findings

Identifies a supersymmetric relation between baryon and meson spectra.

Derives an effective confinement potential from superconformal symmetry.

Shows the massless pion as a special case with no supersymmetric partner.

Abstract

We construct an effective QCD light-front Hamiltonian for both mesons and baryons in the chiral limit based on the generalized supercharges of a superconformal graded algebra. The superconformal construction is shown to be equivalent to a semi-classical approximation to light-front QCD and its embedding in AdS space. The specific breaking of conformal invariance inside the graded algebra uniquely determines the effective confinement potential. The generalized supercharges connect the baryon and meson spectra to each other in a remarkable manner. In particular, the $\pi/b_1$ Regge trajectory is identified as the superpartner of the nucleon trajectory. However, the lowest-lying state on this trajectory, the $\pi$-meson is massless in the chiral limit and has no supersymmetric partner.