Dynamically emergent flavor in a confining theory with unbroken chiral symmetry

I discuss “truncated” QCD studied recently by Glozman et al. through numerical simulations. For two flavors it was observed that truncation restores the full chiral $U(2)\times U(2)$ symmetry of the Lagrangian. Moreover, additional enhancement of the above symmetry connecting representations with distinct Lorentz spins was observed. I argue that the chiral symmetry restoration in a confining theory could entail emergent (extra) dynamical flavors which would show up in the spectrum of color-singlet particles, provided their mass $\ne 0$. As an example, I consider truncated QCD with a single massless Dirac quark. Assuming the validity of the above observations, I demonstrate how a dynamical $SU(2{)}_{\mathrm{fl}}$ symmetry could emerge for massive spin-1 mesons without contradicting general principles.

Figure 1

Chiral symmetry vs number of dimensions and colors. The closed circle shows actual QCD. Crosses denote theories with naturally enhanced chiral symmetry.